size int64 2 8 | keys stringlengths 10 106 | symbols stringlengths 3 29 | domains stringclasses 62
values | pi stringlengths 3 46 | equation stringlengths 10 59 | name stringclasses 19
values | n_const int64 0 4 | n_domains int64 1 6 | max_exp int64 1 34 | exp_l1 int64 2 134 | complexity float64 0 113 | score float64 -104.8 10 | plausible bool 2
classes | exponents stringlengths 27 177 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5 | conductivity,force,length,mass,permeability | m·ℓ·F·μ₀·σ | em,mechanics | m·ℓ⁻³·F⁻¹·μ₀⁻²·σ⁻² | m = k₀ · ℓ³·F·μ₀²·σ² | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "-3", "force": "-1", "permeability": "-2", "conductivity": "-2"} |
5 | force,length,mass,permeability,resistivity | m·ℓ·F·μ₀·ρ_e | em,mechanics | m·ℓ⁻³·F⁻¹·μ₀⁻²·ρ_e² | m = k₀ · ℓ³·F·μ₀²·ρ_e⁻² | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "-3", "force": "-1", "permeability": "-2", "resistivity": "2"} |
5 | conductivity,elem_charge,force,length,mass | m·ℓ·F·σ·e | constants,em,mechanics | m·ℓ⁵·F·σ²·e⁻⁴ | m = k₀ · ℓ⁻⁵·F⁻¹·σ⁻²·e⁴ | null | 1 | 3 | 5 | 13 | 11.8 | -2.8 | false | {"mass": "1", "length": "5", "force": "1", "conductivity": "2", "elem_charge": "-4"} |
5 | elem_charge,force,length,mass,resistivity | m·ℓ·F·ρ_e·e | constants,em,mechanics | m·ℓ⁵·F·ρ_e⁻²·e⁻⁴ | m = k₀ · ℓ⁻⁵·F⁻¹·ρ_e²·e⁴ | null | 1 | 3 | 5 | 13 | 11.8 | -2.8 | false | {"mass": "1", "length": "5", "force": "1", "resistivity": "-2", "elem_charge": "-4"} |
5 | amount,cat_activity,force,length,mass | m·ℓ·F·n·z | chemistry,mechanics | m·ℓ·F⁻¹·n⁻²·z² | m = k₀ · ℓ⁻¹·F·n²·z⁻² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "force": "-1", "amount": "-2", "cat_activity": "2"} |
5 | force,length,mass,molar_energy,molar_mass | m·ℓ·F·M_m·E_m | chemistry,mechanics | m·ℓ⁻¹·F⁻¹·M_m⁻¹·E_m | m = k₀ · ℓ·F·M_m·E_m⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "-1", "force": "-1", "molar_mass": "-1", "molar_energy": "1"} |
5 | cat_activity,force,length,mass,molar_mass | m·ℓ·F·M_m·z | chemistry,mechanics | m·ℓ⁻¹·F·M_m⁻²·z⁻² | m = k₀ · ℓ·F⁻¹·M_m²·z² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "force": "1", "molar_mass": "-2", "cat_activity": "-2"} |
5 | cat_activity,concentration,force,length,mass | m·ℓ·F·c_n·z | chemistry,mechanics | m·ℓ⁻⁵·F⁻¹·c_n⁻²·z² | m = k₀ · ℓ⁵·F·c_n²·z⁻² | null | 0 | 2 | 5 | 11 | 9.8 | -0.3 | false | {"mass": "1", "length": "-5", "force": "-1", "concentration": "-2", "cat_activity": "2"} |
5 | cat_activity,force,length,mass,molar_energy | m·ℓ·F·E_m·z | chemistry,mechanics | m·ℓ⁻¹·F⁻³·E_m²·z² | m = k₀ · ℓ·F³·E_m⁻²·z⁻² | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "-1", "force": "-3", "molar_energy": "2", "cat_activity": "2"} |
6 | boltzmann,cat_activity,force,gas_constant,length,mass | m·ℓ·F·R·z·k_B | chemistry,constants,mechanics | m·ℓ·F⁻¹·R²·z²·k_B⁻² | m = k₀ · ℓ⁻¹·F·R⁻²·z⁻²·k_B² | null | 1 | 3 | 2 | 9 | 7.8 | 1.2 | false | {"mass": "1", "length": "1", "force": "-1", "gas_constant": "2", "cat_activity": "2", "boltzmann": "-2"} |
5 | avogadro,cat_activity,force,length,mass | m·ℓ·F·z·N_A | chemistry,constants,mechanics | m·ℓ·F⁻¹·z²·N_A² | m = k₀ · ℓ⁻¹·F·z⁻²·N_A⁻² | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "1", "force": "-1", "cat_activity": "2", "avogadro": "2"} |
4 | force,length,light_speed,mass | m·ℓ·F·c₀ | constants,mechanics | m·ℓ⁻¹·F⁻¹·c₀² | m = k₀ · ℓ·F·c₀⁻² | null | 1 | 2 | 2 | 5 | 3.8 | 5.7 | true | {"mass": "1", "length": "-1", "force": "-1", "light_speed": "2"} |
4 | force,grav_const,length,mass | m·ℓ·F·G | constants,mechanics | m²·ℓ⁻²·F⁻¹·G | F = k₀ · m²·ℓ⁻²·G | null | 1 | 2 | 2 | 6 | 4.5 | 5 | true | {"mass": "2", "length": "-2", "force": "-1", "grav_const": "1"} |
4 | force,length,mass,planck | m·ℓ·F·h | constants,mechanics | m·ℓ³·F·h⁻² | m = k₀ · ℓ⁻³·F⁻¹·h² | null | 1 | 2 | 3 | 7 | 5.7 | 3.8 | true | {"mass": "1", "length": "3", "force": "1", "planck": "-2"} |
4 | energy,length,mass,power | m·ℓ·E·P | mechanics | m·ℓ²·E⁻³·P² | m = k₀ · ℓ⁻²·E³·P⁻² | null | 0 | 1 | 3 | 8 | 5.8 | 4.2 | true | {"mass": "1", "length": "2", "energy": "-3", "power": "2"} |
4 | ang_momentum,energy,length,mass | m·ℓ·E·Lₐ | mechanics | m·ℓ²·E·Lₐ⁻² | m = k₀ · ℓ⁻²·E⁻¹·Lₐ² | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "2", "energy": "1", "ang_momentum": "-2"} |
4 | action,energy,length,mass | m·ℓ·E·S | mechanics | m·ℓ²·E·S⁻² | m = k₀ · ℓ⁻²·E⁻¹·S² | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "2", "energy": "1", "action": "-2"} |
4 | energy,length,mass,viscosity | m·ℓ·E·μ | mechanics | m·ℓ⁻⁴·E·μ⁻² | m = k₀ · ℓ⁴·E⁻¹·μ² | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "1", "length": "-4", "energy": "1", "viscosity": "-2"} |
4 | energy,kin_viscosity,length,mass | m·ℓ·E·ν | mechanics | m·ℓ⁻²·E⁻¹·ν² | m = k₀ · ℓ²·E·ν⁻² | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "-2", "energy": "-1", "kin_viscosity": "2"} |
4 | energy,length,mass,omega | m·ℓ·E·ω | mechanics | m·ℓ²·E⁻¹·ω² | m = k₀ · ℓ⁻²·E·ω⁻² | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "2", "energy": "-1", "omega": "2"} |
4 | energy,frequency,length,mass | m·ℓ·E·f | mechanics | m·ℓ²·E⁻¹·f² | m = k₀ · ℓ⁻²·E·f⁻² | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "2", "energy": "-1", "frequency": "2"} |
4 | energy,flowrate,length,mass | m·ℓ·E·Q | mechanics | m·ℓ⁻⁴·E⁻¹·Q² | m = k₀ · ℓ⁴·E·Q⁻² | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "1", "length": "-4", "energy": "-1", "flowrate": "2"} |
5 | energy,length,mass,temperature,thermal_cond | m·ℓ·E·Θ·κ | mechanics,thermo | m·ℓ⁴·E⁻³·Θ²·κ² | m = k₀ · ℓ⁻⁴·E³·Θ⁻²·κ⁻² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "1", "length": "4", "energy": "-3", "temperature": "2", "thermal_cond": "2"} |
6 | cat_activity,energy,gas_constant,length,mass,temperature | m·ℓ·E·Θ·R·z | chemistry,mechanics,thermo | m·ℓ²·E⁻³·Θ²·R²·z² | m = k₀ · ℓ⁻²·E³·Θ⁻²·R⁻²·z⁻² | null | 0 | 3 | 3 | 12 | 10.4 | -1.4 | false | {"mass": "1", "length": "2", "energy": "-3", "temperature": "2", "gas_constant": "2", "cat_activity": "2"} |
5 | energy,entropy,length,mass,thermal_cond | m·ℓ·E·S_e·κ | mechanics,thermo | m·ℓ⁴·E⁻¹·S_e⁻²·κ² | m = k₀ · ℓ⁻⁴·E·S_e²·κ⁻² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "4", "energy": "-1", "entropy": "-2", "thermal_cond": "2"} |
6 | cat_activity,energy,entropy,gas_constant,length,mass | m·ℓ·E·S_e·R·z | chemistry,mechanics,thermo | m·ℓ²·E⁻¹·S_e⁻²·R²·z² | m = k₀ · ℓ⁻²·E·S_e²·R⁻²·z⁻² | null | 0 | 3 | 2 | 10 | 8.5 | 0.5 | false | {"mass": "1", "length": "2", "energy": "-1", "entropy": "-2", "gas_constant": "2", "cat_activity": "2"} |
5 | energy,heat_capacity,length,mass,thermal_cond | m·ℓ·E·C·κ | mechanics,thermo | m·ℓ⁴·E⁻¹·C⁻²·κ² | m = k₀ · ℓ⁻⁴·E·C²·κ⁻² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "4", "energy": "-1", "heat_capacity": "-2", "thermal_cond": "2"} |
6 | cat_activity,energy,gas_constant,heat_capacity,length,mass | m·ℓ·E·C·R·z | chemistry,mechanics,thermo | m·ℓ²·E⁻¹·C⁻²·R²·z² | m = k₀ · ℓ⁻²·E·C²·R⁻²·z⁻² | null | 0 | 3 | 2 | 10 | 8.5 | 0.5 | false | {"mass": "1", "length": "2", "energy": "-1", "heat_capacity": "-2", "gas_constant": "2", "cat_activity": "2"} |
5 | energy,length,mass,specific_heat,thermal_cond | m·ℓ·E·c·κ | mechanics,thermo | m·ℓ⁻⁴·E·c²·κ⁻² | m = k₀ · ℓ⁴·E⁻¹·c⁻²·κ² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "-4", "energy": "1", "specific_heat": "2", "thermal_cond": "-2"} |
6 | cat_activity,energy,gas_constant,length,mass,specific_heat | m·ℓ·E·c·R·z | chemistry,mechanics,thermo | m·ℓ⁻²·E·c²·R⁻²·z⁻² | m = k₀ · ℓ²·E⁻¹·c⁻²·R²·z² | null | 0 | 3 | 2 | 10 | 8.5 | 0.5 | false | {"mass": "1", "length": "-2", "energy": "1", "specific_heat": "2", "gas_constant": "-2", "cat_activity": "-2"} |
5 | energy,expansion,length,mass,thermal_cond | m·ℓ·E·κ·β | mechanics,thermo | m·ℓ⁴·E⁻³·κ²·β⁻² | m = k₀ · ℓ⁻⁴·E³·κ⁻²·β² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "1", "length": "4", "energy": "-3", "thermal_cond": "2", "expansion": "-2"} |
6 | amount,energy,gas_constant,length,mass,thermal_cond | m·ℓ·E·κ·n·R | chemistry,mechanics,thermo | m·ℓ⁴·E⁻¹·κ²·n⁻²·R⁻² | m = k₀ · ℓ⁻⁴·E·κ⁻²·n²·R² | null | 0 | 3 | 4 | 12 | 10.9 | -1.9 | false | {"mass": "1", "length": "4", "energy": "-1", "thermal_cond": "2", "amount": "-2", "gas_constant": "-2"} |
6 | energy,gas_constant,length,mass,molar_mass,thermal_cond | m·ℓ·E·κ·M_m·R | chemistry,mechanics,thermo | m·ℓ⁻⁴·E·κ⁻²·M_m⁻²·R² | m = k₀ · ℓ⁴·E⁻¹·κ²·M_m²·R⁻² | null | 0 | 3 | 4 | 12 | 10.9 | -1.9 | false | {"mass": "1", "length": "-4", "energy": "1", "thermal_cond": "-2", "molar_mass": "-2", "gas_constant": "2"} |
6 | concentration,energy,gas_constant,length,mass,thermal_cond | m·ℓ·E·κ·c_n·R | chemistry,mechanics,thermo | m·ℓ⁻²·E⁻¹·κ²·c_n⁻²·R⁻² | m = k₀ · ℓ²·E·κ⁻²·c_n²·R² | null | 0 | 3 | 2 | 10 | 8.5 | 0.5 | false | {"mass": "1", "length": "-2", "energy": "-1", "thermal_cond": "2", "concentration": "-2", "gas_constant": "-2"} |
6 | energy,gas_constant,length,mass,molar_energy,thermal_cond | m·ℓ·E·κ·E_m·R | chemistry,mechanics,thermo | m·ℓ⁴·E⁻³·κ²·E_m²·R⁻² | m = k₀ · ℓ⁻⁴·E³·κ⁻²·E_m⁻²·R² | null | 0 | 3 | 4 | 14 | 12.3 | -3.3 | false | {"mass": "1", "length": "4", "energy": "-3", "thermal_cond": "2", "molar_energy": "2", "gas_constant": "-2"} |
6 | avogadro,energy,gas_constant,length,mass,thermal_cond | m·ℓ·E·κ·R·N_A | chemistry,constants,mechanics,thermo | m·ℓ⁴·E⁻¹·κ²·R⁻²·N_A² | m = k₀ · ℓ⁻⁴·E·κ⁻²·R²·N_A⁻² | null | 1 | 4 | 4 | 12 | 11.5 | -3 | false | {"mass": "1", "length": "4", "energy": "-1", "thermal_cond": "2", "gas_constant": "-2", "avogadro": "2"} |
5 | boltzmann,energy,length,mass,thermal_cond | m·ℓ·E·κ·k_B | constants,mechanics,thermo | m·ℓ⁴·E⁻¹·κ²·k_B⁻² | m = k₀ · ℓ⁻⁴·E·κ⁻²·k_B² | null | 1 | 3 | 4 | 10 | 9.2 | -0.2 | false | {"mass": "1", "length": "4", "energy": "-1", "thermal_cond": "2", "boltzmann": "-2"} |
4 | energy,length,mass,thermal_diff | m·ℓ·E·α | mechanics,thermo | m·ℓ⁻²·E⁻¹·α² | m = k₀ · ℓ²·E·α⁻² | null | 0 | 2 | 2 | 6 | 4.5 | 5 | true | {"mass": "1", "length": "-2", "energy": "-1", "thermal_diff": "2"} |
6 | cat_activity,energy,expansion,gas_constant,length,mass | m·ℓ·E·β·R·z | chemistry,mechanics,thermo | m·ℓ²·E⁻³·β⁻²·R²·z² | m = k₀ · ℓ⁻²·E³·β²·R⁻²·z⁻² | null | 0 | 3 | 3 | 12 | 10.4 | -1.4 | false | {"mass": "1", "length": "2", "energy": "-3", "expansion": "-2", "gas_constant": "2", "cat_activity": "2"} |
5 | charge,current,energy,length,mass | m·ℓ·E·q·i | em,mechanics | m·ℓ²·E⁻¹·q⁻²·i² | m = k₀ · ℓ⁻²·E·q²·i⁻² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "energy": "-1", "charge": "-2", "current": "2"} |
5 | charge,energy,length,mass,resistance | m·ℓ·E·q·R | em,mechanics | m·ℓ²·E·q⁻⁴·R⁻² | m = k₀ · ℓ⁻²·E⁻¹·q⁴·R² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "2", "energy": "1", "charge": "-4", "resistance": "-2"} |
5 | bfield,charge,energy,length,mass | m·ℓ·E·q·B | em,mechanics | m·ℓ⁻²·E·q⁻²·B⁻² | m = k₀ · ℓ²·E⁻¹·q²·B² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "-2", "energy": "1", "charge": "-2", "bfield": "-2"} |
5 | charge,energy,length,mag_flux,mass | m·ℓ·E·q·Φ | em,mechanics | m·ℓ²·E·q⁻²·Φ⁻² | m = k₀ · ℓ⁻²·E⁻¹·q²·Φ² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "energy": "1", "charge": "-2", "mag_flux": "-2"} |
5 | charge,conductivity,energy,length,mass | m·ℓ·E·q·σ | em,mechanics | m·ℓ⁴·E·q⁻⁴·σ² | m = k₀ · ℓ⁻⁴·E⁻¹·q⁴·σ⁻² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "1", "length": "4", "energy": "1", "charge": "-4", "conductivity": "2"} |
5 | charge,energy,length,mass,resistivity | m·ℓ·E·q·ρ_e | em,mechanics | m·ℓ⁴·E·q⁻⁴·ρ_e⁻² | m = k₀ · ℓ⁻⁴·E⁻¹·q⁴·ρ_e² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "1", "length": "4", "energy": "1", "charge": "-4", "resistivity": "-2"} |
5 | current,energy,length,mass,voltage | m·ℓ·E·i·U | em,mechanics | m·ℓ²·E⁻³·i²·U² | m = k₀ · ℓ⁻²·E³·i⁻²·U⁻² | null | 0 | 2 | 3 | 10 | 8.1 | 1.4 | false | {"mass": "1", "length": "2", "energy": "-3", "current": "2", "voltage": "2"} |
5 | current,energy,length,mass,resistance | m·ℓ·E·i·R | em,mechanics | m·ℓ²·E⁻³·i⁴·R² | m = k₀ · ℓ⁻²·E³·i⁻⁴·R⁻² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "1", "length": "2", "energy": "-3", "current": "4", "resistance": "2"} |
5 | capacitance,current,energy,length,mass | m·ℓ·E·i·C_e | em,mechanics | m·ℓ²·E⁻²·i²·C_e⁻¹ | m = k₀ · ℓ⁻²·E²·i⁻²·C_e | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "energy": "-2", "current": "2", "capacitance": "-1"} |
5 | current,efield,energy,length,mass | m·ℓ·E·i·E_f | em,mechanics | m·ℓ⁴·E⁻³·i²·E_f² | m = k₀ · ℓ⁻⁴·E³·i⁻²·E_f⁻² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "1", "length": "4", "energy": "-3", "current": "2", "efield": "2"} |
5 | current,energy,length,mass,permittivity | m·ℓ·E·i·ε | em,mechanics | m·ℓ·E⁻²·i²·ε⁻¹ | m = k₀ · ℓ⁻¹·E²·i⁻²·ε | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "energy": "-2", "current": "2", "permittivity": "-1"} |
5 | current,elem_charge,energy,length,mass | m·ℓ·E·i·e | constants,em,mechanics | m·ℓ²·E⁻¹·i²·e⁻² | m = k₀ · ℓ⁻²·E·i⁻²·e² | null | 1 | 3 | 2 | 8 | 6.8 | 2.2 | false | {"mass": "1", "length": "2", "energy": "-1", "current": "2", "elem_charge": "-2"} |
5 | energy,length,mass,resistance,voltage | m·ℓ·E·U·R | em,mechanics | m·ℓ²·E⁻³·U⁴·R⁻² | m = k₀ · ℓ⁻²·E³·U⁻⁴·R² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "1", "length": "2", "energy": "-3", "voltage": "4", "resistance": "-2"} |
5 | energy,inductance,length,mass,voltage | m·ℓ·E·U·L_e | em,mechanics | m·ℓ²·E⁻²·U²·L_e⁻¹ | m = k₀ · ℓ⁻²·E²·U⁻²·L_e | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "energy": "-2", "voltage": "2", "inductance": "-1"} |
5 | bfield,energy,length,mass,voltage | m·ℓ·E·U·B | em,mechanics | m·ℓ⁻²·E⁻¹·U²·B⁻² | m = k₀ · ℓ²·E·U⁻²·B² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "-2", "energy": "-1", "voltage": "2", "bfield": "-2"} |
5 | energy,length,mag_flux,mass,voltage | m·ℓ·E·U·Φ | em,mechanics | m·ℓ²·E⁻¹·U²·Φ⁻² | m = k₀ · ℓ⁻²·E·U⁻²·Φ² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "energy": "-1", "voltage": "2", "mag_flux": "-2"} |
5 | energy,length,mass,permeability,voltage | m·ℓ·E·U·μ₀ | em,mechanics | m·ℓ·E⁻²·U²·μ₀⁻¹ | m = k₀ · ℓ⁻¹·E²·U⁻²·μ₀ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "energy": "-2", "voltage": "2", "permeability": "-1"} |
5 | conductivity,energy,length,mass,voltage | m·ℓ·E·U·σ | em,mechanics | m·ℓ⁴·E⁻³·U⁴·σ² | m = k₀ · ℓ⁻⁴·E³·U⁻⁴·σ⁻² | null | 0 | 2 | 4 | 14 | 11.4 | -1.9 | false | {"mass": "1", "length": "4", "energy": "-3", "voltage": "4", "conductivity": "2"} |
5 | energy,length,mass,resistivity,voltage | m·ℓ·E·U·ρ_e | em,mechanics | m·ℓ⁴·E⁻³·U⁴·ρ_e⁻² | m = k₀ · ℓ⁻⁴·E³·U⁻⁴·ρ_e² | null | 0 | 2 | 4 | 14 | 11.4 | -1.9 | false | {"mass": "1", "length": "4", "energy": "-3", "voltage": "4", "resistivity": "-2"} |
5 | capacitance,energy,length,mass,resistance | m·ℓ·E·R·C_e | em,mechanics | m·ℓ²·E⁻¹·R⁻²·C_e⁻² | m = k₀ · ℓ⁻²·E·R²·C_e² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "energy": "-1", "resistance": "-2", "capacitance": "-2"} |
5 | energy,inductance,length,mass,resistance | m·ℓ·E·R·L_e | em,mechanics | m·ℓ²·E⁻¹·R²·L_e⁻² | m = k₀ · ℓ⁻²·E·R⁻²·L_e² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "energy": "-1", "resistance": "2", "inductance": "-2"} |
5 | efield,energy,length,mass,resistance | m·ℓ·E·R·E_f | em,mechanics | m·ℓ⁶·E⁻³·R⁻²·E_f⁴ | m = k₀ · ℓ⁻⁶·E³·R²·E_f⁻⁴ | null | 0 | 2 | 6 | 16 | 13.8 | -4.3 | false | {"mass": "1", "length": "6", "energy": "-3", "resistance": "-2", "efield": "4"} |
5 | bfield,energy,length,mass,resistance | m·ℓ·E·R·B | em,mechanics | m·ℓ⁻⁶·E·R²·B⁻⁴ | m = k₀ · ℓ⁶·E⁻¹·R⁻²·B⁴ | null | 0 | 2 | 6 | 14 | 12.4 | -2.9 | false | {"mass": "1", "length": "-6", "energy": "1", "resistance": "2", "bfield": "-4"} |
5 | energy,length,mag_flux,mass,resistance | m·ℓ·E·R·Φ | em,mechanics | m·ℓ²·E·R²·Φ⁻⁴ | m = k₀ · ℓ⁻²·E⁻¹·R⁻²·Φ⁴ | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "2", "energy": "1", "resistance": "2", "mag_flux": "-4"} |
5 | elem_charge,energy,length,mass,resistance | m·ℓ·E·R·e | constants,em,mechanics | m·ℓ²·E·R⁻²·e⁻⁴ | m = k₀ · ℓ⁻²·E⁻¹·R²·e⁴ | null | 1 | 3 | 4 | 10 | 9.2 | -0.2 | false | {"mass": "1", "length": "2", "energy": "1", "resistance": "-2", "elem_charge": "-4"} |
5 | capacitance,energy,inductance,length,mass | m·ℓ·E·C_e·L_e | em,mechanics | m·ℓ²·E⁻¹·C_e⁻¹·L_e⁻¹ | m = k₀ · ℓ⁻²·E·C_e·L_e | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "energy": "-1", "capacitance": "-1", "inductance": "-1"} |
5 | capacitance,energy,length,mass,permeability | m·ℓ·E·C_e·μ₀ | em,mechanics | m·ℓ·E⁻¹·C_e⁻¹·μ₀⁻¹ | m = k₀ · ℓ⁻¹·E·C_e·μ₀ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "energy": "-1", "capacitance": "-1", "permeability": "-1"} |
5 | capacitance,conductivity,energy,length,mass | m·ℓ·E·C_e·σ | em,mechanics | m·ℓ⁴·E⁻¹·C_e⁻²·σ² | m = k₀ · ℓ⁻⁴·E·C_e²·σ⁻² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "4", "energy": "-1", "capacitance": "-2", "conductivity": "2"} |
5 | capacitance,energy,length,mass,resistivity | m·ℓ·E·C_e·ρ_e | em,mechanics | m·ℓ⁴·E⁻¹·C_e⁻²·ρ_e⁻² | m = k₀ · ℓ⁻⁴·E·C_e²·ρ_e² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "4", "energy": "-1", "capacitance": "-2", "resistivity": "-2"} |
5 | efield,energy,inductance,length,mass | m·ℓ·E·L_e·E_f | em,mechanics | m·ℓ⁴·E⁻²·L_e⁻¹·E_f² | m = k₀ · ℓ⁻⁴·E²·L_e·E_f⁻² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "4", "energy": "-2", "inductance": "-1", "efield": "2"} |
5 | energy,inductance,length,mass,permittivity | m·ℓ·E·L_e·ε | em,mechanics | m·ℓ·E⁻¹·L_e⁻¹·ε⁻¹ | m = k₀ · ℓ⁻¹·E·L_e·ε | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "energy": "-1", "inductance": "-1", "permittivity": "-1"} |
5 | efield,energy,length,mag_flux,mass | m·ℓ·E·E_f·Φ | em,mechanics | m·ℓ⁴·E⁻¹·E_f²·Φ⁻² | m = k₀ · ℓ⁻⁴·E·E_f⁻²·Φ² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "4", "energy": "-1", "efield": "2", "mag_flux": "-2"} |
5 | efield,energy,length,mass,permeability | m·ℓ·E·E_f·μ₀ | em,mechanics | m·ℓ³·E⁻²·E_f²·μ₀⁻¹ | m = k₀ · ℓ⁻³·E²·E_f⁻²·μ₀ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "3", "energy": "-2", "efield": "2", "permeability": "-1"} |
5 | conductivity,efield,energy,length,mass | m·ℓ·E·E_f·σ | em,mechanics | m·ℓ⁸·E⁻³·E_f⁴·σ² | m = k₀ · ℓ⁻⁸·E³·E_f⁻⁴·σ⁻² | null | 0 | 2 | 8 | 18 | 16.2 | -6.7 | false | {"mass": "1", "length": "8", "energy": "-3", "efield": "4", "conductivity": "2"} |
5 | efield,energy,length,mass,resistivity | m·ℓ·E·E_f·ρ_e | em,mechanics | m·ℓ⁸·E⁻³·E_f⁴·ρ_e⁻² | m = k₀ · ℓ⁻⁸·E³·E_f⁻⁴·ρ_e² | null | 0 | 2 | 8 | 18 | 16.2 | -6.7 | false | {"mass": "1", "length": "8", "energy": "-3", "efield": "4", "resistivity": "-2"} |
5 | bfield,conductivity,energy,length,mass | m·ℓ·E·B·σ | em,mechanics | m·ℓ⁻⁸·E·B⁻⁴·σ⁻² | m = k₀ · ℓ⁸·E⁻¹·B⁴·σ² | null | 0 | 2 | 8 | 16 | 14.8 | -5.3 | false | {"mass": "1", "length": "-8", "energy": "1", "bfield": "-4", "conductivity": "-2"} |
5 | bfield,energy,length,mass,resistivity | m·ℓ·E·B·ρ_e | em,mechanics | m·ℓ⁻⁸·E·B⁻⁴·ρ_e² | m = k₀ · ℓ⁸·E⁻¹·B⁴·ρ_e⁻² | null | 0 | 2 | 8 | 16 | 14.8 | -5.3 | false | {"mass": "1", "length": "-8", "energy": "1", "bfield": "-4", "resistivity": "2"} |
5 | bfield,elem_charge,energy,length,mass | m·ℓ·E·B·e | constants,em,mechanics | m·ℓ⁻²·E·B⁻²·e⁻² | m = k₀ · ℓ²·E⁻¹·B²·e² | null | 1 | 3 | 2 | 8 | 6.8 | 2.2 | false | {"mass": "1", "length": "-2", "energy": "1", "bfield": "-2", "elem_charge": "-2"} |
5 | elem_charge,energy,length,mag_flux,mass | m·ℓ·E·Φ·e | constants,em,mechanics | m·ℓ²·E·Φ⁻²·e⁻² | m = k₀ · ℓ⁻²·E⁻¹·Φ²·e² | null | 1 | 3 | 2 | 8 | 6.8 | 2.2 | false | {"mass": "1", "length": "2", "energy": "1", "mag_flux": "-2", "elem_charge": "-2"} |
5 | conductivity,energy,length,mass,permittivity | m·ℓ·E·ε·σ | em,mechanics | m·ℓ²·E⁻¹·ε⁻²·σ² | m = k₀ · ℓ⁻²·E·ε²·σ⁻² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "energy": "-1", "permittivity": "-2", "conductivity": "2"} |
5 | energy,length,mass,permittivity,resistivity | m·ℓ·E·ε·ρ_e | em,mechanics | m·ℓ²·E⁻¹·ε⁻²·ρ_e⁻² | m = k₀ · ℓ⁻²·E·ε²·ρ_e² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "energy": "-1", "permittivity": "-2", "resistivity": "-2"} |
5 | conductivity,energy,length,mass,permeability | m·ℓ·E·μ₀·σ | em,mechanics | m·ℓ⁻²·E⁻¹·μ₀⁻²·σ⁻² | m = k₀ · ℓ²·E·μ₀²·σ² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "-2", "energy": "-1", "permeability": "-2", "conductivity": "-2"} |
5 | energy,length,mass,permeability,resistivity | m·ℓ·E·μ₀·ρ_e | em,mechanics | m·ℓ⁻²·E⁻¹·μ₀⁻²·ρ_e² | m = k₀ · ℓ²·E·μ₀²·ρ_e⁻² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "-2", "energy": "-1", "permeability": "-2", "resistivity": "2"} |
5 | conductivity,elem_charge,energy,length,mass | m·ℓ·E·σ·e | constants,em,mechanics | m·ℓ⁴·E·σ²·e⁻⁴ | m = k₀ · ℓ⁻⁴·E⁻¹·σ⁻²·e⁴ | null | 1 | 3 | 4 | 12 | 10.6 | -1.6 | false | {"mass": "1", "length": "4", "energy": "1", "conductivity": "2", "elem_charge": "-4"} |
5 | elem_charge,energy,length,mass,resistivity | m·ℓ·E·ρ_e·e | constants,em,mechanics | m·ℓ⁴·E·ρ_e⁻²·e⁻⁴ | m = k₀ · ℓ⁻⁴·E⁻¹·ρ_e²·e⁴ | null | 1 | 3 | 4 | 12 | 10.6 | -1.6 | false | {"mass": "1", "length": "4", "energy": "1", "resistivity": "-2", "elem_charge": "-4"} |
5 | amount,cat_activity,energy,length,mass | m·ℓ·E·n·z | chemistry,mechanics | m·ℓ²·E⁻¹·n⁻²·z² | m = k₀ · ℓ⁻²·E·n²·z⁻² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "energy": "-1", "amount": "-2", "cat_activity": "2"} |
5 | cat_activity,energy,length,mass,molar_mass | m·ℓ·E·M_m·z | chemistry,mechanics | m·ℓ⁻²·E·M_m⁻²·z⁻² | m = k₀ · ℓ²·E⁻¹·M_m²·z² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "-2", "energy": "1", "molar_mass": "-2", "cat_activity": "-2"} |
5 | cat_activity,concentration,energy,length,mass | m·ℓ·E·c_n·z | chemistry,mechanics | m·ℓ⁻⁴·E⁻¹·c_n⁻²·z² | m = k₀ · ℓ⁴·E·c_n²·z⁻² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "-4", "energy": "-1", "concentration": "-2", "cat_activity": "2"} |
5 | cat_activity,energy,length,mass,molar_energy | m·ℓ·E·E_m·z | chemistry,mechanics | m·ℓ²·E⁻³·E_m²·z² | m = k₀ · ℓ⁻²·E³·E_m⁻²·z⁻² | null | 0 | 2 | 3 | 10 | 8.1 | 1.4 | false | {"mass": "1", "length": "2", "energy": "-3", "molar_energy": "2", "cat_activity": "2"} |
6 | boltzmann,cat_activity,energy,gas_constant,length,mass | m·ℓ·E·R·z·k_B | chemistry,constants,mechanics | m·ℓ²·E⁻¹·R²·z²·k_B⁻² | m = k₀ · ℓ⁻²·E·R⁻²·z⁻²·k_B² | null | 1 | 3 | 2 | 10 | 8.5 | 0.5 | false | {"mass": "1", "length": "2", "energy": "-1", "gas_constant": "2", "cat_activity": "2", "boltzmann": "-2"} |
5 | avogadro,cat_activity,energy,length,mass | m·ℓ·E·z·N_A | chemistry,constants,mechanics | m·ℓ²·E⁻¹·z²·N_A² | m = k₀ · ℓ⁻²·E·z⁻²·N_A⁻² | null | 1 | 3 | 2 | 8 | 6.8 | 2.2 | false | {"mass": "1", "length": "2", "energy": "-1", "cat_activity": "2", "avogadro": "2"} |
4 | energy,grav_const,length,mass | m·ℓ·E·G | constants,mechanics | m²·ℓ⁻¹·E⁻¹·G | ℓ = k₀ · m²·E⁻¹·G | null | 1 | 2 | 2 | 5 | 3.8 | 5.7 | true | {"mass": "2", "length": "-1", "energy": "-1", "grav_const": "1"} |
4 | energy,length,mass,planck | m·ℓ·E·h | constants,mechanics | m·ℓ²·E·h⁻² | m = k₀ · ℓ⁻²·E⁻¹·h² | null | 1 | 2 | 2 | 6 | 4.5 | 5 | true | {"mass": "1", "length": "2", "energy": "1", "planck": "-2"} |
4 | length,mass,power,torque | m·ℓ·τ·P | mechanics | m·ℓ²·τ⁻³·P² | m = k₀ · ℓ⁻²·τ³·P⁻² | null | 0 | 1 | 3 | 8 | 5.8 | 4.2 | true | {"mass": "1", "length": "2", "torque": "-3", "power": "2"} |
4 | ang_momentum,length,mass,torque | m·ℓ·τ·Lₐ | mechanics | m·ℓ²·τ·Lₐ⁻² | m = k₀ · ℓ⁻²·τ⁻¹·Lₐ² | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "2", "torque": "1", "ang_momentum": "-2"} |
4 | action,length,mass,torque | m·ℓ·τ·S | mechanics | m·ℓ²·τ·S⁻² | m = k₀ · ℓ⁻²·τ⁻¹·S² | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "2", "torque": "1", "action": "-2"} |
4 | length,mass,torque,viscosity | m·ℓ·τ·μ | mechanics | m·ℓ⁻⁴·τ·μ⁻² | m = k₀ · ℓ⁴·τ⁻¹·μ² | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "1", "length": "-4", "torque": "1", "viscosity": "-2"} |
4 | kin_viscosity,length,mass,torque | m·ℓ·τ·ν | mechanics | m·ℓ⁻²·τ⁻¹·ν² | m = k₀ · ℓ²·τ·ν⁻² | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "-2", "torque": "-1", "kin_viscosity": "2"} |
4 | length,mass,omega,torque | m·ℓ·τ·ω | mechanics | m·ℓ²·τ⁻¹·ω² | m = k₀ · ℓ⁻²·τ·ω⁻² | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "2", "torque": "-1", "omega": "2"} |
4 | frequency,length,mass,torque | m·ℓ·τ·f | mechanics | m·ℓ²·τ⁻¹·f² | m = k₀ · ℓ⁻²·τ·f⁻² | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "2", "torque": "-1", "frequency": "2"} |
4 | flowrate,length,mass,torque | m·ℓ·τ·Q | mechanics | m·ℓ⁻⁴·τ⁻¹·Q² | m = k₀ · ℓ⁴·τ·Q⁻² | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "1", "length": "-4", "torque": "-1", "flowrate": "2"} |
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