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 | avogadro,illuminance,light_speed,lum_intensity,molar_energy,planck | E_m·I_v·E_v·c₀·h·N_A | chemistry,constants,photometry | E_m²·I_v·E_v⁻¹·c₀⁻²·h⁻²·N_A⁻² | I_v = k₀ · E_m⁻²·E_v·c₀²·h²·N_A² | null | 3 | 3 | 2 | 10 | 10.5 | -4.5 | false | {"molar_energy": "2", "lum_intensity": "1", "illuminance": "-1", "light_speed": "-2", "planck": "-2", "avogadro": "-2"} |
6 | avogadro,grav_const,illuminance,lum_intensity,molar_energy,planck | E_m·I_v·E_v·G·h·N_A | chemistry,constants,photometry | E_m⁶·I_v⁵·E_v⁻⁵·G⁻²·h⁻⁸·N_A⁻⁶ | G = k₀ · E_m³·I_v⁵ᐟ²·E_v⁻⁵ᐟ²·h⁻⁴·N_A⁻³ | null | 3 | 3 | 8 | 32 | 28.9 | -22.9 | false | {"molar_energy": "6", "lum_intensity": "5", "illuminance": "-5", "grav_const": "-2", "planck": "-8", "avogadro": "-6"} |
6 | avogadro,grav_const,light_speed,lum_intensity,luminance,molar_energy | E_m·I_v·L_v·c₀·G·N_A | chemistry,constants,photometry | E_m²·I_v⁻¹·L_v·c₀⁻⁸·G²·N_A⁻² | I_v = k₀ · E_m²·L_v·c₀⁻⁸·G²·N_A⁻² | null | 3 | 3 | 8 | 16 | 17.7 | -11.7 | false | {"molar_energy": "2", "lum_intensity": "-1", "luminance": "1", "light_speed": "-8", "grav_const": "2", "avogadro": "-2"} |
6 | avogadro,light_speed,lum_intensity,luminance,molar_energy,planck | E_m·I_v·L_v·c₀·h·N_A | chemistry,constants,photometry | E_m²·I_v·L_v⁻¹·c₀⁻²·h⁻²·N_A⁻² | I_v = k₀ · E_m⁻²·L_v·c₀²·h²·N_A² | null | 3 | 3 | 2 | 10 | 10.5 | -4.5 | false | {"molar_energy": "2", "lum_intensity": "1", "luminance": "-1", "light_speed": "-2", "planck": "-2", "avogadro": "-2"} |
6 | avogadro,grav_const,lum_intensity,luminance,molar_energy,planck | E_m·I_v·L_v·G·h·N_A | chemistry,constants,photometry | E_m⁶·I_v⁵·L_v⁻⁵·G⁻²·h⁻⁸·N_A⁻⁶ | G = k₀ · E_m³·I_v⁵ᐟ²·L_v⁻⁵ᐟ²·h⁻⁴·N_A⁻³ | null | 3 | 3 | 8 | 32 | 28.9 | -22.9 | false | {"molar_energy": "6", "lum_intensity": "5", "luminance": "-5", "grav_const": "-2", "planck": "-8", "avogadro": "-6"} |
5 | avogadro,grav_const,light_speed,molar_energy,planck | E_m·c₀·G·h·N_A | chemistry,constants | E_m²·c₀⁻⁵·G·h⁻¹·N_A⁻² | G = k₀ · E_m⁻²·c₀⁵·h·N_A² | null | 4 | 2 | 5 | 11 | 12.8 | -7.8 | false | {"molar_energy": "2", "light_speed": "-5", "grav_const": "1", "planck": "-1", "avogadro": "-2"} |
6 | boltzmann,cat_activity,gas_constant,illuminance,light_speed,lum_intensity | R·z·I_v·E_v·c₀·k_B | chemistry,constants,photometry | R²·z²·I_v·E_v⁻¹·c₀⁻²·k_B⁻² | I_v = k₀ · R⁻²·z⁻²·E_v·c₀²·k_B² | null | 2 | 3 | 2 | 10 | 9.5 | -2 | false | {"gas_constant": "2", "cat_activity": "2", "lum_intensity": "1", "illuminance": "-1", "light_speed": "-2", "boltzmann": "-2"} |
7 | boltzmann,cat_activity,gas_constant,grav_const,illuminance,lum_intensity,planck | R·z·I_v·E_v·G·h·k_B | chemistry,constants,photometry | R⁶·z⁶·I_v⁵·E_v⁻⁵·G⁻²·h⁻²·k_B⁻⁶ | G = k₀ · R³·z³·I_v⁵ᐟ²·E_v⁻⁵ᐟ²·h⁻¹·k_B⁻³ | null | 3 | 3 | 6 | 32 | 28.2 | -22.2 | false | {"gas_constant": "6", "cat_activity": "6", "lum_intensity": "5", "illuminance": "-5", "grav_const": "-2", "planck": "-2", "boltzmann": "-6"} |
6 | boltzmann,cat_activity,gas_constant,light_speed,lum_intensity,luminance | R·z·I_v·L_v·c₀·k_B | chemistry,constants,photometry | R²·z²·I_v·L_v⁻¹·c₀⁻²·k_B⁻² | I_v = k₀ · R⁻²·z⁻²·L_v·c₀²·k_B² | null | 2 | 3 | 2 | 10 | 9.5 | -2 | false | {"gas_constant": "2", "cat_activity": "2", "lum_intensity": "1", "luminance": "-1", "light_speed": "-2", "boltzmann": "-2"} |
7 | boltzmann,cat_activity,gas_constant,grav_const,lum_intensity,luminance,planck | R·z·I_v·L_v·G·h·k_B | chemistry,constants,photometry | R⁶·z⁶·I_v⁵·L_v⁻⁵·G⁻²·h⁻²·k_B⁻⁶ | G = k₀ · R³·z³·I_v⁵ᐟ²·L_v⁻⁵ᐟ²·h⁻¹·k_B⁻³ | null | 3 | 3 | 6 | 32 | 28.2 | -22.2 | false | {"gas_constant": "6", "cat_activity": "6", "lum_intensity": "5", "luminance": "-5", "grav_const": "-2", "planck": "-2", "boltzmann": "-6"} |
6 | boltzmann,cat_activity,gas_constant,grav_const,light_speed,planck | R·z·c₀·G·h·k_B | chemistry,constants | R²·z²·c₀⁻⁵·G·h·k_B⁻² | G = k₀ · R⁻²·z⁻²·c₀⁵·h⁻¹·k_B² | null | 4 | 2 | 5 | 13 | 14.5 | -9.5 | false | {"gas_constant": "2", "cat_activity": "2", "light_speed": "-5", "grav_const": "1", "planck": "1", "boltzmann": "-2"} |
3 | avogadro,boltzmann,gas_constant | R·k_B·N_A | chemistry,constants | R·k_B⁻¹·N_A⁻¹ | R = k₀ · k_B·N_A | null | 2 | 2 | 1 | 3 | 2.6 | 5.4 | false | {"gas_constant": "1", "boltzmann": "-1", "avogadro": "-1"} |
5 | avogadro,cat_activity,illuminance,light_speed,lum_intensity | z·I_v·E_v·c₀·N_A | chemistry,constants,photometry | z²·I_v·E_v⁻¹·c₀⁻²·N_A² | I_v = k₀ · z⁻²·E_v·c₀²·N_A⁻² | null | 2 | 3 | 2 | 8 | 7.8 | -0.3 | false | {"cat_activity": "2", "lum_intensity": "1", "illuminance": "-1", "light_speed": "-2", "avogadro": "2"} |
6 | avogadro,cat_activity,grav_const,illuminance,lum_intensity,planck | z·I_v·E_v·G·h·N_A | chemistry,constants,photometry | z⁶·I_v⁵·E_v⁻⁵·G⁻²·h⁻²·N_A⁶ | G = k₀ · z³·I_v⁵ᐟ²·E_v⁻⁵ᐟ²·h⁻¹·N_A³ | null | 3 | 3 | 6 | 26 | 23.7 | -17.7 | false | {"cat_activity": "6", "lum_intensity": "5", "illuminance": "-5", "grav_const": "-2", "planck": "-2", "avogadro": "6"} |
5 | avogadro,cat_activity,light_speed,lum_intensity,luminance | z·I_v·L_v·c₀·N_A | chemistry,constants,photometry | z²·I_v·L_v⁻¹·c₀⁻²·N_A² | I_v = k₀ · z⁻²·L_v·c₀²·N_A⁻² | null | 2 | 3 | 2 | 8 | 7.8 | -0.3 | false | {"cat_activity": "2", "lum_intensity": "1", "luminance": "-1", "light_speed": "-2", "avogadro": "2"} |
6 | avogadro,cat_activity,grav_const,lum_intensity,luminance,planck | z·I_v·L_v·G·h·N_A | chemistry,constants,photometry | z⁶·I_v⁵·L_v⁻⁵·G⁻²·h⁻²·N_A⁶ | G = k₀ · z³·I_v⁵ᐟ²·L_v⁻⁵ᐟ²·h⁻¹·N_A³ | null | 3 | 3 | 6 | 26 | 23.7 | -17.7 | false | {"cat_activity": "6", "lum_intensity": "5", "luminance": "-5", "grav_const": "-2", "planck": "-2", "avogadro": "6"} |
5 | avogadro,cat_activity,grav_const,light_speed,planck | z·c₀·G·h·N_A | chemistry,constants | z²·c₀⁻⁵·G·h·N_A² | G = k₀ · z⁻²·c₀⁵·h⁻¹·N_A⁻² | null | 4 | 2 | 5 | 11 | 12.8 | -7.8 | false | {"cat_activity": "2", "light_speed": "-5", "grav_const": "1", "planck": "1", "avogadro": "2"} |
5 | grav_const,illuminance,light_speed,lum_intensity,planck | I_v·E_v·c₀·G·h | constants,photometry | I_v·E_v⁻¹·c₀³·G⁻¹·h⁻¹ | I_v = k₀ · E_v·c₀⁻³·G·h | null | 3 | 2 | 3 | 7 | 8 | -1.5 | false | {"lum_intensity": "1", "illuminance": "-1", "light_speed": "3", "grav_const": "-1", "planck": "-1"} |
5 | grav_const,light_speed,lum_intensity,luminance,planck | I_v·L_v·c₀·G·h | constants,photometry | I_v·L_v⁻¹·c₀³·G⁻¹·h⁻¹ | I_v = k₀ · L_v·c₀⁻³·G·h | null | 3 | 2 | 3 | 7 | 8 | -1.5 | false | {"lum_intensity": "1", "luminance": "-1", "light_speed": "3", "grav_const": "-1", "planck": "-1"} |
2 | illuminance,luminance | E_v·L_v | photometry | E_v·L_v⁻¹ | E_v = k₀ · L_v | null | 0 | 1 | 1 | 2 | 0 | 10 | true | {"illuminance": "1", "luminance": "-1"} |
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