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"}