Datasets:
RANDMEDIATION
/
PhysicsBabel

Dataset card Data Studio Files
xet
 Community
1
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
6
concentration,expansion,gas_constant,length,mass,velocity
m·ℓ·v·β·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻³·v²·β·c_n⁻¹·R⁻¹
m = k₀ · ℓ³·v⁻²·β⁻¹·c_n·R
null
0
3
3
9
8.3
0.7
false
{"mass": "1", "length": "-3", "velocity": "2", "expansion": "1", "concentration": "-1", "gas_constant": "-1"}
6
cat_activity,expansion,gas_constant,length,mass,velocity
m·ℓ·v·β·R·z
chemistry,mechanics,thermo
m·ℓ⁻¹·v³·β·R⁻¹·z⁻¹
m = k₀ · ℓ·v⁻³·β⁻¹·R·z
null
0
3
3
8
7.6
1.4
false
{"mass": "1", "length": "-1", "velocity": "3", "expansion": "1", "gas_constant": "-1", "cat_activity": "-1"}
5
charge,length,mass,resistance,velocity
m·ℓ·v·q·R
em,mechanics
m·ℓ·v·q⁻²·R⁻¹
m = k₀ · ℓ⁻¹·v⁻¹·q²·R
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "1", "velocity": "1", "charge": "-2", "resistance": "-1"}
5
charge,efield,length,mass,velocity
m·ℓ·v·q·E_f
em,mechanics
m·ℓ⁻¹·v²·q⁻¹·E_f⁻¹
m = k₀ · ℓ·v⁻²·q·E_f
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-1", "velocity": "2", "charge": "-1", "efield": "-1"}
5
bfield,charge,length,mass,velocity
m·ℓ·v·q·B
em,mechanics
m·ℓ⁻¹·v·q⁻¹·B⁻¹
m = k₀ · ℓ·v⁻¹·q·B
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "-1", "velocity": "1", "charge": "-1", "bfield": "-1"}
5
charge,length,mag_flux,mass,velocity
m·ℓ·v·q·Φ
em,mechanics
m·ℓ·v·q⁻¹·Φ⁻¹
m = k₀ · ℓ⁻¹·v⁻¹·q·Φ
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "velocity": "1", "charge": "-1", "mag_flux": "-1"}
5
charge,length,mass,permittivity,velocity
m·ℓ·v·q·ε
em,mechanics
m·ℓ·v²·q⁻²·ε
m = k₀ · ℓ⁻¹·v⁻²·q²·ε⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "velocity": "2", "charge": "-2", "permittivity": "1"}
5
charge,conductivity,length,mass,velocity
m·ℓ·v·q·σ
em,mechanics
m·ℓ²·v·q⁻²·σ
m = k₀ · ℓ⁻²·v⁻¹·q²·σ⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "velocity": "1", "charge": "-2", "conductivity": "1"}
5
charge,length,mass,resistivity,velocity
m·ℓ·v·q·ρ_e
em,mechanics
m·ℓ²·v·q⁻²·ρ_e⁻¹
m = k₀ · ℓ⁻²·v⁻¹·q²·ρ_e
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "velocity": "1", "charge": "-2", "resistivity": "-1"}
5
current,length,mass,velocity,voltage
m·ℓ·v·i·U
em,mechanics
m·ℓ⁻¹·v³·i⁻¹·U⁻¹
m = k₀ · ℓ·v⁻³·i·U
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "-1", "velocity": "3", "current": "-1", "voltage": "-1"}
5
current,length,mass,resistance,velocity
m·ℓ·v·i·R
em,mechanics
m·ℓ⁻¹·v³·i⁻²·R⁻¹
m = k₀ · ℓ·v⁻³·i²·R
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "-1", "velocity": "3", "current": "-2", "resistance": "-1"}
5
capacitance,current,length,mass,velocity
m·ℓ·v·i·C_e
em,mechanics
m·ℓ⁻²·v⁴·i⁻²·C_e
m = k₀ · ℓ²·v⁻⁴·i²·C_e⁻¹
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-2", "velocity": "4", "current": "-2", "capacitance": "1"}
5
current,efield,length,mass,velocity
m·ℓ·v·i·E_f
em,mechanics
m·ℓ⁻²·v³·i⁻¹·E_f⁻¹
m = k₀ · ℓ²·v⁻³·i·E_f
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "-2", "velocity": "3", "current": "-1", "efield": "-1"}
5
bfield,current,length,mass,velocity
m·ℓ·v·i·B
em,mechanics
m·ℓ⁻²·v²·i⁻¹·B⁻¹
m = k₀ · ℓ²·v⁻²·i·B
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-2", "velocity": "2", "current": "-1", "bfield": "-1"}
5
current,length,mass,permittivity,velocity
m·ℓ·v·i·ε
em,mechanics
m·ℓ⁻¹·v⁴·i⁻²·ε
m = k₀ · ℓ·v⁻⁴·i²·ε⁻¹
null
0
2
4
9
7.9
1.6
false
{"mass": "1", "length": "-1", "velocity": "4", "current": "-2", "permittivity": "1"}
5
current,length,mass,permeability,velocity
m·ℓ·v·i·μ₀
em,mechanics
m·ℓ⁻¹·v²·i⁻²·μ₀⁻¹
m = k₀ · ℓ·v⁻²·i²·μ₀
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-1", "velocity": "2", "current": "-2", "permeability": "-1"}
5
length,mass,resistance,velocity,voltage
m·ℓ·v·U·R
em,mechanics
m·ℓ⁻¹·v³·U⁻²·R
m = k₀ · ℓ·v⁻³·U²·R⁻¹
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "-1", "velocity": "3", "voltage": "-2", "resistance": "1"}
5
inductance,length,mass,velocity,voltage
m·ℓ·v·U·L_e
em,mechanics
m·ℓ⁻²·v⁴·U⁻²·L_e
m = k₀ · ℓ²·v⁻⁴·U²·L_e⁻¹
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-2", "velocity": "4", "voltage": "-2", "inductance": "1"}
5
length,mass,permittivity,velocity,voltage
m·ℓ·v·U·ε
em,mechanics
m·ℓ⁻¹·v²·U⁻²·ε⁻¹
m = k₀ · ℓ·v⁻²·U²·ε
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-1", "velocity": "2", "voltage": "-2", "permittivity": "-1"}
5
length,mass,permeability,velocity,voltage
m·ℓ·v·U·μ₀
em,mechanics
m·ℓ⁻¹·v⁴·U⁻²·μ₀
m = k₀ · ℓ·v⁻⁴·U²·μ₀⁻¹
null
0
2
4
9
7.9
1.6
false
{"mass": "1", "length": "-1", "velocity": "4", "voltage": "-2", "permeability": "1"}
5
conductivity,length,mass,velocity,voltage
m·ℓ·v·U·σ
em,mechanics
m·ℓ⁻²·v³·U⁻²·σ⁻¹
m = k₀ · ℓ²·v⁻³·U²·σ
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-2", "velocity": "3", "voltage": "-2", "conductivity": "-1"}
5
length,mass,resistivity,velocity,voltage
m·ℓ·v·U·ρ_e
em,mechanics
m·ℓ⁻²·v³·U⁻²·ρ_e
m = k₀ · ℓ²·v⁻³·U²·ρ_e⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-2", "velocity": "3", "voltage": "-2", "resistivity": "1"}
5
efield,length,mass,resistance,velocity
m·ℓ·v·R·E_f
em,mechanics
m·ℓ⁻³·v³·R·E_f⁻²
m = k₀ · ℓ³·v⁻³·R⁻¹·E_f²
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "-3", "velocity": "3", "resistance": "1", "efield": "-2"}
5
bfield,length,mass,resistance,velocity
m·ℓ·v·R·B
em,mechanics
m·ℓ⁻³·v·R·B⁻²
m = k₀ · ℓ³·v⁻¹·R⁻¹·B²
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "-3", "velocity": "1", "resistance": "1", "bfield": "-2"}
5
length,mag_flux,mass,resistance,velocity
m·ℓ·v·R·Φ
em,mechanics
m·ℓ·v·R·Φ⁻²
m = k₀ · ℓ⁻¹·v⁻¹·R⁻¹·Φ²
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "1", "velocity": "1", "resistance": "1", "mag_flux": "-2"}
5
elem_charge,length,mass,resistance,velocity
m·ℓ·v·R·e
constants,em,mechanics
m·ℓ·v·R⁻¹·e⁻²
m = k₀ · ℓ⁻¹·v⁻¹·R·e²
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "1", "velocity": "1", "resistance": "-1", "elem_charge": "-2"}
5
capacitance,efield,length,mass,velocity
m·ℓ·v·C_e·E_f
em,mechanics
m·ℓ⁻²·v²·C_e⁻¹·E_f⁻²
m = k₀ · ℓ²·v⁻²·C_e·E_f²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "velocity": "2", "capacitance": "-1", "efield": "-2"}
5
efield,inductance,length,mass,velocity
m·ℓ·v·L_e·E_f
em,mechanics
m·ℓ⁻⁴·v⁴·L_e·E_f⁻²
m = k₀ · ℓ⁴·v⁻⁴·L_e⁻¹·E_f²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "-4", "velocity": "4", "inductance": "1", "efield": "-2"}
5
bfield,inductance,length,mass,velocity
m·ℓ·v·L_e·B
em,mechanics
m·ℓ⁻⁴·v²·L_e·B⁻²
m = k₀ · ℓ⁴·v⁻²·L_e⁻¹·B²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "velocity": "2", "inductance": "1", "bfield": "-2"}
5
efield,length,mass,permittivity,velocity
m·ℓ·v·E_f·ε
em,mechanics
m·ℓ⁻³·v²·E_f⁻²·ε⁻¹
m = k₀ · ℓ³·v⁻²·E_f²·ε
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-3", "velocity": "2", "efield": "-2", "permittivity": "-1"}
5
efield,length,mass,permeability,velocity
m·ℓ·v·E_f·μ₀
em,mechanics
m·ℓ⁻³·v⁴·E_f⁻²·μ₀
m = k₀ · ℓ³·v⁻⁴·E_f²·μ₀⁻¹
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "-3", "velocity": "4", "efield": "-2", "permeability": "1"}
5
conductivity,efield,length,mass,velocity
m·ℓ·v·E_f·σ
em,mechanics
m·ℓ⁻⁴·v³·E_f⁻²·σ⁻¹
m = k₀ · ℓ⁴·v⁻³·E_f²·σ
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "-4", "velocity": "3", "efield": "-2", "conductivity": "-1"}
5
efield,length,mass,resistivity,velocity
m·ℓ·v·E_f·ρ_e
em,mechanics
m·ℓ⁻⁴·v³·E_f⁻²·ρ_e
m = k₀ · ℓ⁴·v⁻³·E_f²·ρ_e⁻¹
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "-4", "velocity": "3", "efield": "-2", "resistivity": "1"}
5
efield,elem_charge,length,mass,velocity
m·ℓ·v·E_f·e
constants,em,mechanics
m·ℓ⁻¹·v²·E_f⁻¹·e⁻¹
m = k₀ · ℓ·v⁻²·E_f·e
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "-1", "velocity": "2", "efield": "-1", "elem_charge": "-1"}
5
bfield,length,mass,permeability,velocity
m·ℓ·v·B·μ₀
em,mechanics
m·ℓ⁻³·v²·B⁻²·μ₀
m = k₀ · ℓ³·v⁻²·B²·μ₀⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-3", "velocity": "2", "bfield": "-2", "permeability": "1"}
5
bfield,conductivity,length,mass,velocity
m·ℓ·v·B·σ
em,mechanics
m·ℓ⁻⁴·v·B⁻²·σ⁻¹
m = k₀ · ℓ⁴·v⁻¹·B²·σ
null
0
2
4
9
7.9
1.6
false
{"mass": "1", "length": "-4", "velocity": "1", "bfield": "-2", "conductivity": "-1"}
5
bfield,length,mass,resistivity,velocity
m·ℓ·v·B·ρ_e
em,mechanics
m·ℓ⁻⁴·v·B⁻²·ρ_e
m = k₀ · ℓ⁴·v⁻¹·B²·ρ_e⁻¹
null
0
2
4
9
7.9
1.6
false
{"mass": "1", "length": "-4", "velocity": "1", "bfield": "-2", "resistivity": "1"}
5
bfield,elem_charge,length,mass,velocity
m·ℓ·v·B·e
constants,em,mechanics
m·ℓ⁻¹·v·B⁻¹·e⁻¹
m = k₀ · ℓ·v⁻¹·B·e
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "-1", "velocity": "1", "bfield": "-1", "elem_charge": "-1"}
5
length,mag_flux,mass,permeability,velocity
m·ℓ·v·Φ·μ₀
em,mechanics
m·ℓ·v²·Φ⁻²·μ₀
m = k₀ · ℓ⁻¹·v⁻²·Φ²·μ₀⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "velocity": "2", "mag_flux": "-2", "permeability": "1"}
5
elem_charge,length,mag_flux,mass,velocity
m·ℓ·v·Φ·e
constants,em,mechanics
m·ℓ·v·Φ⁻¹·e⁻¹
m = k₀ · ℓ⁻¹·v⁻¹·Φ·e
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "1", "velocity": "1", "mag_flux": "-1", "elem_charge": "-1"}
5
elem_charge,length,mass,permittivity,velocity
m·ℓ·v·ε·e
constants,em,mechanics
m·ℓ·v²·ε·e⁻²
m = k₀ · ℓ⁻¹·v⁻²·ε⁻¹·e²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "1", "velocity": "2", "permittivity": "1", "elem_charge": "-2"}
5
conductivity,elem_charge,length,mass,velocity
m·ℓ·v·σ·e
constants,em,mechanics
m·ℓ²·v·σ·e⁻²
m = k₀ · ℓ⁻²·v⁻¹·σ⁻¹·e²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "velocity": "1", "conductivity": "1", "elem_charge": "-2"}
5
elem_charge,length,mass,resistivity,velocity
m·ℓ·v·ρ_e·e
constants,em,mechanics
m·ℓ²·v·ρ_e⁻¹·e⁻²
m = k₀ · ℓ⁻²·v⁻¹·ρ_e·e²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "velocity": "1", "resistivity": "-1", "elem_charge": "-2"}
5
cat_activity,length,mass,molar_mass,velocity
m·ℓ·v·M_m·z
chemistry,mechanics
m·ℓ⁻¹·v·M_m⁻¹·z⁻¹
m = k₀ · ℓ·v⁻¹·M_m·z
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "-1", "velocity": "1", "molar_mass": "-1", "cat_activity": "-1"}
5
concentration,length,mass,molar_energy,velocity
m·ℓ·v·c_n·E_m
chemistry,mechanics
m·ℓ⁻³·v²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ³·v⁻²·c_n·E_m
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "-3", "velocity": "2", "concentration": "-1", "molar_energy": "-1"}
5
cat_activity,length,mass,molar_energy,velocity
m·ℓ·v·E_m·z
chemistry,mechanics
m·ℓ⁻¹·v³·E_m⁻¹·z⁻¹
m = k₀ · ℓ·v⁻³·E_m·z
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "-1", "velocity": "3", "molar_energy": "-1", "cat_activity": "-1"}
4
grav_const,length,mass,velocity
m·ℓ·v·G
constants,mechanics
m·ℓ⁻¹·v⁻²·G
m = k₀ · ℓ·v²·G⁻¹
null
1
2
2
5
3.8
5.7
true
{"mass": "1", "length": "-1", "velocity": "-2", "grav_const": "1"}
4
length,mass,planck,velocity
m·ℓ·v·h
constants,mechanics
m·ℓ·v·h⁻¹
m = k₀ · ℓ⁻¹·v⁻¹·h
null
1
2
1
4
2.6
6.9
true
{"mass": "1", "length": "1", "velocity": "1", "planck": "-1"}
4
acceleration,energy,length,mass
m·ℓ·a·E
mechanics
m·ℓ·a·E⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·E
null
0
1
1
4
2
8
true
{"mass": "1", "length": "1", "acceleration": "1", "energy": "-1"}
4
acceleration,length,mass,torque
m·ℓ·a·τ
mechanics
m·ℓ·a·τ⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·τ
null
0
1
1
4
2
8
true
{"mass": "1", "length": "1", "acceleration": "1", "torque": "-1"}
4
acceleration,length,mass,power
m·ℓ·a·P
mechanics
m²·ℓ·a³·P⁻²
ℓ = k₀ · m⁻²·a⁻³·P²
null
0
1
3
8
5.8
4.2
true
{"mass": "2", "length": "1", "acceleration": "3", "power": "-2"}
4
acceleration,length,mass,momentum
m·ℓ·a·p
mechanics
m²·ℓ·a·p⁻²
ℓ = k₀ · m⁻²·a⁻¹·p²
null
0
1
2
6
3.9
6.1
true
{"mass": "2", "length": "1", "acceleration": "1", "momentum": "-2"}
4
acceleration,ang_momentum,length,mass
m·ℓ·a·Lₐ
mechanics
m²·ℓ³·a·Lₐ⁻²
a = k₀ · m⁻²·ℓ⁻³·Lₐ²
null
0
1
3
8
5.8
4.2
true
{"mass": "2", "length": "3", "acceleration": "1", "ang_momentum": "-2"}
4
acceleration,action,length,mass
m·ℓ·a·S
mechanics
m²·ℓ³·a·S⁻²
a = k₀ · m⁻²·ℓ⁻³·S²
null
0
1
3
8
5.8
4.2
true
{"mass": "2", "length": "3", "acceleration": "1", "action": "-2"}
4
acceleration,length,mass,pressure
m·ℓ·a·P_p
mechanics
m·ℓ⁻²·a·P_p⁻¹
m = k₀ · ℓ²·a⁻¹·P_p
null
0
1
2
5
3.2
6.8
true
{"mass": "1", "length": "-2", "acceleration": "1", "pressure": "-1"}
4
acceleration,length,mass,viscosity
m·ℓ·a·μ
mechanics
m²·ℓ⁻³·a·μ⁻²
a = k₀ · m⁻²·ℓ³·μ²
null
0
1
3
8
5.8
4.2
true
{"mass": "2", "length": "-3", "acceleration": "1", "viscosity": "-2"}
4
acceleration,length,mass,stiffness
m·ℓ·a·k
mechanics
m·ℓ⁻¹·a·k⁻¹
m = k₀ · ℓ·a⁻¹·k
null
0
1
1
4
2
8
true
{"mass": "1", "length": "-1", "acceleration": "1", "stiffness": "-1"}
4
acceleration,length,mass,surf_tension
m·ℓ·a·γ
mechanics
m·ℓ⁻¹·a·γ⁻¹
m = k₀ · ℓ·a⁻¹·γ
null
0
1
1
4
2
8
true
{"mass": "1", "length": "-1", "acceleration": "1", "surf_tension": "-1"}
5
acceleration,entropy,length,mass,temperature
m·ℓ·a·Θ·S_e
mechanics,thermo
m·ℓ·a·Θ⁻¹·S_e⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·Θ·S_e
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "acceleration": "1", "temperature": "-1", "entropy": "-1"}
5
acceleration,heat_capacity,length,mass,temperature
m·ℓ·a·Θ·C
mechanics,thermo
m·ℓ·a·Θ⁻¹·C⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·Θ·C
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "acceleration": "1", "temperature": "-1", "heat_capacity": "-1"}
5
acceleration,length,mass,temperature,thermal_cond
m·ℓ·a·Θ·κ
mechanics,thermo
m²·ℓ⁻¹·a³·Θ⁻²·κ⁻²
ℓ = k₀ · m²·a³·Θ⁻²·κ⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "-1", "acceleration": "3", "temperature": "-2", "thermal_cond": "-2"}
6
acceleration,amount,gas_constant,length,mass,temperature
m·ℓ·a·Θ·n·R
chemistry,mechanics,thermo
m·ℓ·a·Θ⁻¹·n⁻¹·R⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·Θ·n·R
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "acceleration": "1", "temperature": "-1", "amount": "-1", "gas_constant": "-1"}
6
acceleration,concentration,gas_constant,length,mass,temperature
m·ℓ·a·Θ·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻²·a·Θ⁻¹·c_n⁻¹·R⁻¹
m = k₀ · ℓ²·a⁻¹·Θ·c_n·R
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "acceleration": "1", "temperature": "-1", "concentration": "-1", "gas_constant": "-1"}
6
acceleration,cat_activity,gas_constant,length,mass,temperature
m·ℓ·a·Θ·R·z
chemistry,mechanics,thermo
m²·ℓ·a³·Θ⁻²·R⁻²·z⁻²
ℓ = k₀ · m⁻²·a⁻³·Θ²·R²·z²
null
0
3
3
12
10.4
-1.4
false
{"mass": "2", "length": "1", "acceleration": "3", "temperature": "-2", "gas_constant": "-2", "cat_activity": "-2"}
6
acceleration,avogadro,gas_constant,length,mass,temperature
m·ℓ·a·Θ·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ·a·Θ⁻¹·R⁻¹·N_A
m = k₀ · ℓ⁻¹·a⁻¹·Θ·R·N_A⁻¹
null
1
4
1
6
5.8
2.7
false
{"mass": "1", "length": "1", "acceleration": "1", "temperature": "-1", "gas_constant": "-1", "avogadro": "1"}
5
acceleration,boltzmann,length,mass,temperature
m·ℓ·a·Θ·k_B
constants,mechanics,thermo
m·ℓ·a·Θ⁻¹·k_B⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·Θ·k_B
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "1", "acceleration": "1", "temperature": "-1", "boltzmann": "-1"}
5
acceleration,entropy,expansion,length,mass
m·ℓ·a·S_e·β
mechanics,thermo
m·ℓ·a·S_e⁻¹·β
m = k₀ · ℓ⁻¹·a⁻¹·S_e·β⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "acceleration": "1", "entropy": "-1", "expansion": "1"}
6
acceleration,entropy,gas_constant,length,mass,molar_energy
m·ℓ·a·S_e·E_m·R
chemistry,mechanics,thermo
m·ℓ·a·S_e⁻¹·E_m⁻¹·R
m = k₀ · ℓ⁻¹·a⁻¹·S_e·E_m·R⁻¹
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "acceleration": "1", "entropy": "-1", "molar_energy": "-1", "gas_constant": "1"}
5
acceleration,expansion,heat_capacity,length,mass
m·ℓ·a·C·β
mechanics,thermo
m·ℓ·a·C⁻¹·β
m = k₀ · ℓ⁻¹·a⁻¹·C·β⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "acceleration": "1", "heat_capacity": "-1", "expansion": "1"}
6
acceleration,gas_constant,heat_capacity,length,mass,molar_energy
m·ℓ·a·C·E_m·R
chemistry,mechanics,thermo
m·ℓ·a·C⁻¹·E_m⁻¹·R
m = k₀ · ℓ⁻¹·a⁻¹·C·E_m·R⁻¹
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "acceleration": "1", "heat_capacity": "-1", "molar_energy": "-1", "gas_constant": "1"}
5
acceleration,length,mass,specific_heat,thermal_cond
m·ℓ·a·c·κ
mechanics,thermo
m²·ℓ⁻³·a·c²·κ⁻²
a = k₀ · m⁻²·ℓ³·c⁻²·κ²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "-3", "acceleration": "1", "specific_heat": "2", "thermal_cond": "-2"}
6
acceleration,cat_activity,gas_constant,length,mass,specific_heat
m·ℓ·a·c·R·z
chemistry,mechanics,thermo
m²·ℓ⁻¹·a·c²·R⁻²·z⁻²
ℓ = k₀ · m²·a·c²·R⁻²·z⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "2", "length": "-1", "acceleration": "1", "specific_heat": "2", "gas_constant": "-2", "cat_activity": "-2"}
5
acceleration,expansion,length,mass,thermal_cond
m·ℓ·a·κ·β
mechanics,thermo
m²·ℓ⁻¹·a³·κ⁻²·β²
ℓ = k₀ · m²·a³·κ⁻²·β²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "-1", "acceleration": "3", "thermal_cond": "-2", "expansion": "2"}
6
acceleration,gas_constant,length,mass,molar_mass,thermal_cond
m·ℓ·a·κ·M_m·R
chemistry,mechanics,thermo
m²·ℓ⁻³·a·κ⁻²·M_m⁻²·R²
a = k₀ · m⁻²·ℓ³·κ²·M_m²·R⁻²
null
0
3
3
12
10.4
-1.4
false
{"mass": "2", "length": "-3", "acceleration": "1", "thermal_cond": "-2", "molar_mass": "-2", "gas_constant": "2"}
6
acceleration,gas_constant,length,mass,molar_energy,thermal_cond
m·ℓ·a·κ·E_m·R
chemistry,mechanics,thermo
m²·ℓ⁻¹·a³·κ⁻²·E_m⁻²·R²
ℓ = k₀ · m²·a³·κ⁻²·E_m⁻²·R²
null
0
3
3
12
10.4
-1.4
false
{"mass": "2", "length": "-1", "acceleration": "3", "thermal_cond": "-2", "molar_energy": "-2", "gas_constant": "2"}
6
acceleration,amount,expansion,gas_constant,length,mass
m·ℓ·a·β·n·R
chemistry,mechanics,thermo
m·ℓ·a·β·n⁻¹·R⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·β⁻¹·n·R
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "acceleration": "1", "expansion": "1", "amount": "-1", "gas_constant": "-1"}
6
acceleration,concentration,expansion,gas_constant,length,mass
m·ℓ·a·β·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻²·a·β·c_n⁻¹·R⁻¹
m = k₀ · ℓ²·a⁻¹·β⁻¹·c_n·R
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "acceleration": "1", "expansion": "1", "concentration": "-1", "gas_constant": "-1"}
6
acceleration,cat_activity,expansion,gas_constant,length,mass
m·ℓ·a·β·R·z
chemistry,mechanics,thermo
m²·ℓ·a³·β²·R⁻²·z⁻²
ℓ = k₀ · m⁻²·a⁻³·β⁻²·R²·z²
null
0
3
3
12
10.4
-1.4
false
{"mass": "2", "length": "1", "acceleration": "3", "expansion": "2", "gas_constant": "-2", "cat_activity": "-2"}
6
acceleration,avogadro,expansion,gas_constant,length,mass
m·ℓ·a·β·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ·a·β·R⁻¹·N_A
m = k₀ · ℓ⁻¹·a⁻¹·β⁻¹·R·N_A⁻¹
null
1
4
1
6
5.8
2.7
false
{"mass": "1", "length": "1", "acceleration": "1", "expansion": "1", "gas_constant": "-1", "avogadro": "1"}
5
acceleration,boltzmann,expansion,length,mass
m·ℓ·a·β·k_B
constants,mechanics,thermo
m·ℓ·a·β·k_B⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·β⁻¹·k_B
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "1", "acceleration": "1", "expansion": "1", "boltzmann": "-1"}
5
acceleration,charge,length,mass,voltage
m·ℓ·a·q·U
em,mechanics
m·ℓ·a·q⁻¹·U⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·q·U
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "acceleration": "1", "charge": "-1", "voltage": "-1"}
5
acceleration,charge,length,mass,resistance
m·ℓ·a·q·R
em,mechanics
m²·ℓ³·a·q⁻⁴·R⁻²
a = k₀ · m⁻²·ℓ⁻³·q⁴·R²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "3", "acceleration": "1", "charge": "-4", "resistance": "-2"}
5
acceleration,capacitance,charge,length,mass
m·ℓ·a·q·C_e
em,mechanics
m·ℓ·a·q⁻²·C_e
m = k₀ · ℓ⁻¹·a⁻¹·q²·C_e⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "1", "acceleration": "1", "charge": "-2", "capacitance": "1"}
5
acceleration,bfield,charge,length,mass
m·ℓ·a·q·B
em,mechanics
m²·ℓ⁻¹·a·q⁻²·B⁻²
ℓ = k₀ · m²·a·q⁻²·B⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "length": "-1", "acceleration": "1", "charge": "-2", "bfield": "-2"}
5
acceleration,charge,length,mag_flux,mass
m·ℓ·a·q·Φ
em,mechanics
m²·ℓ³·a·q⁻²·Φ⁻²
a = k₀ · m⁻²·ℓ⁻³·q²·Φ²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "3", "acceleration": "1", "charge": "-2", "mag_flux": "-2"}
5
acceleration,charge,length,mass,permittivity
m·ℓ·a·q·ε
em,mechanics
m·ℓ²·a·q⁻²·ε
m = k₀ · ℓ⁻²·a⁻¹·q²·ε⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "acceleration": "1", "charge": "-2", "permittivity": "1"}
5
acceleration,charge,conductivity,length,mass
m·ℓ·a·q·σ
em,mechanics
m²·ℓ⁵·a·q⁻⁴·σ²
a = k₀ · m⁻²·ℓ⁻⁵·q⁴·σ⁻²
null
0
2
5
14
11.9
-2.4
false
{"mass": "2", "length": "5", "acceleration": "1", "charge": "-4", "conductivity": "2"}
5
acceleration,charge,length,mass,resistivity
m·ℓ·a·q·ρ_e
em,mechanics
m²·ℓ⁵·a·q⁻⁴·ρ_e⁻²
a = k₀ · m⁻²·ℓ⁻⁵·q⁴·ρ_e²
null
0
2
5
14
11.9
-2.4
false
{"mass": "2", "length": "5", "acceleration": "1", "charge": "-4", "resistivity": "-2"}
5
acceleration,current,length,mass,voltage
m·ℓ·a·i·U
em,mechanics
m²·ℓ·a³·i⁻²·U⁻²
ℓ = k₀ · m⁻²·a⁻³·i²·U²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "1", "acceleration": "3", "current": "-2", "voltage": "-2"}
5
acceleration,current,length,mass,resistance
m·ℓ·a·i·R
em,mechanics
m²·ℓ·a³·i⁻⁴·R⁻²
ℓ = k₀ · m⁻²·a⁻³·i⁴·R²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "1", "acceleration": "3", "current": "-4", "resistance": "-2"}
5
acceleration,current,inductance,length,mass
m·ℓ·a·i·L_e
em,mechanics
m·ℓ·a·i⁻²·L_e⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·i²·L_e
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "1", "acceleration": "1", "current": "-2", "inductance": "-1"}
5
acceleration,current,efield,length,mass
m·ℓ·a·i·E_f
em,mechanics
m²·ℓ⁻¹·a³·i⁻²·E_f⁻²
ℓ = k₀ · m²·a³·i⁻²·E_f⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "-1", "acceleration": "3", "current": "-2", "efield": "-2"}
5
acceleration,bfield,current,length,mass
m·ℓ·a·i·B
em,mechanics
m·ℓ⁻¹·a·i⁻¹·B⁻¹
m = k₀ · ℓ·a⁻¹·i·B
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "-1", "acceleration": "1", "current": "-1", "bfield": "-1"}
5
acceleration,current,length,mag_flux,mass
m·ℓ·a·i·Φ
em,mechanics
m·ℓ·a·i⁻¹·Φ⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·i·Φ
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "acceleration": "1", "current": "-1", "mag_flux": "-1"}
5
acceleration,current,length,mass,permittivity
m·ℓ·a·i·ε
em,mechanics
m·ℓ·a²·i⁻²·ε
m = k₀ · ℓ⁻¹·a⁻²·i²·ε⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "acceleration": "2", "current": "-2", "permittivity": "1"}
5
acceleration,conductivity,current,length,mass
m·ℓ·a·i·σ
em,mechanics
m²·ℓ³·a³·i⁻⁴·σ²
m = k₀ · ℓ⁻³ᐟ²·a⁻³ᐟ²·i²·σ⁻¹
null
0
2
4
14
11.4
-1.9
false
{"mass": "2", "length": "3", "acceleration": "3", "current": "-4", "conductivity": "2"}
5
acceleration,current,length,mass,resistivity
m·ℓ·a·i·ρ_e
em,mechanics
m²·ℓ³·a³·i⁻⁴·ρ_e⁻²
m = k₀ · ℓ⁻³ᐟ²·a⁻³ᐟ²·i²·ρ_e
null
0
2
4
14
11.4
-1.9
false
{"mass": "2", "length": "3", "acceleration": "3", "current": "-4", "resistivity": "-2"}
5
acceleration,length,mass,resistance,voltage
m·ℓ·a·U·R
em,mechanics
m²·ℓ·a³·U⁻⁴·R²
ℓ = k₀ · m⁻²·a⁻³·U⁴·R⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "1", "acceleration": "3", "voltage": "-4", "resistance": "2"}
5
acceleration,capacitance,length,mass,voltage
m·ℓ·a·U·C_e
em,mechanics
m·ℓ·a·U⁻²·C_e⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·U²·C_e
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "1", "acceleration": "1", "voltage": "-2", "capacitance": "-1"}
5
acceleration,length,mass,permeability,voltage
m·ℓ·a·U·μ₀
em,mechanics
m·ℓ·a²·U⁻²·μ₀
m = k₀ · ℓ⁻¹·a⁻²·U²·μ₀⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "acceleration": "2", "voltage": "-2", "permeability": "1"}