Average Error: 23.9 → 3.2
Time: 57.8s
Precision: 64
$\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{Vat}}{Vat}\right)}^{\left(\frac{1}{3}\right)} \cdot Dvac\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(EFvac - \frac{\left(2 \cdot Gama\right) \cdot Vat}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot Vat}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{KB \cdot T}}$
$\begin{array}{l} \mathbf{if}\;T \cdot KB \le 4.999127391294479 \cdot 10^{+286}:\\ \;\;\;\;\left(\frac{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \left(\sqrt[3]{\pi \cdot 48} \cdot \sqrt[3]{\frac{1}{Vat}}\right)}{e^{\frac{EFvac - \frac{Gama \cdot Vat}{\frac{\sqrt[3]{\frac{1 + i}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{T \cdot KB}}} \cdot Dvac\right) \cdot \sqrt[3]{1 + i}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{1 + i} \cdot \left(Dvac \cdot \left(\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{48}{\frac{Vat}{\pi}}}\right)\right)\\ \end{array}$
\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{Vat}}{Vat}\right)}^{\left(\frac{1}{3}\right)} \cdot Dvac\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(EFvac - \frac{\left(2 \cdot Gama\right) \cdot Vat}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot Vat}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{KB \cdot T}}
\begin{array}{l}
\mathbf{if}\;T \cdot KB \le 4.999127391294479 \cdot 10^{+286}:\\
\;\;\;\;\left(\frac{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \left(\sqrt[3]{\pi \cdot 48} \cdot \sqrt[3]{\frac{1}{Vat}}\right)}{e^{\frac{EFvac - \frac{Gama \cdot Vat}{\frac{\sqrt[3]{\frac{1 + i}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{T \cdot KB}}} \cdot Dvac\right) \cdot \sqrt[3]{1 + i}\\

\mathbf{else}:\\
\;\;\;\;\sqrt[3]{1 + i} \cdot \left(Dvac \cdot \left(\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{48}{\frac{Vat}{\pi}}}\right)\right)\\

\end{array}
double f(double Vat, double Dvac, double i, double EFvac, double Gama, double KB, double T) {
double r34687875 = 48.0;
double r34687876 = atan2(1.0, 0.0);
double r34687877 = r34687875 * r34687876;
double r34687878 = r34687877 * r34687876;
double r34687879 = Vat;
double r34687880 = r34687878 / r34687879;
double r34687881 = r34687880 / r34687879;
double r34687882 = 1.0;
double r34687883 = 3.0;
double r34687884 = r34687882 / r34687883;
double r34687885 = pow(r34687881, r34687884);
double r34687886 = Dvac;
double r34687887 = r34687885 * r34687886;
double r34687888 = i;
double r34687889 = r34687888 + r34687882;
double r34687890 = pow(r34687889, r34687884);
double r34687891 = r34687887 * r34687890;
double r34687892 = EFvac;
double r34687893 = 2.0;
double r34687894 = Gama;
double r34687895 = r34687893 * r34687894;
double r34687896 = r34687895 * r34687879;
double r34687897 = r34687883 * r34687889;
double r34687898 = r34687897 * r34687879;
double r34687899 = 4.0;
double r34687900 = r34687899 * r34687876;
double r34687901 = r34687898 / r34687900;
double r34687902 = pow(r34687901, r34687884);
double r34687903 = r34687896 / r34687902;
double r34687904 = r34687892 - r34687903;
double r34687905 = -r34687904;
double r34687906 = KB;
double r34687907 = T;
double r34687908 = r34687906 * r34687907;
double r34687909 = r34687905 / r34687908;
double r34687910 = exp(r34687909);
double r34687911 = r34687891 * r34687910;
return r34687911;
}


double f(double Vat, double Dvac, double i, double EFvac, double Gama, double KB, double T) {
double r34687912 = T;
double r34687913 = KB;
double r34687914 = r34687912 * r34687913;
double r34687915 = 4.999127391294479e+286;
bool r34687916 = r34687914 <= r34687915;
double r34687917 = 1.0;
double r34687918 = Vat;
double r34687919 = atan2(1.0, 0.0);
double r34687920 = r34687918 / r34687919;
double r34687921 = r34687917 / r34687920;
double r34687922 = cbrt(r34687921);
double r34687923 = 48.0;
double r34687924 = r34687919 * r34687923;
double r34687925 = cbrt(r34687924);
double r34687926 = r34687917 / r34687918;
double r34687927 = cbrt(r34687926);
double r34687928 = r34687925 * r34687927;
double r34687929 = r34687922 * r34687928;
double r34687930 = EFvac;
double r34687931 = Gama;
double r34687932 = r34687931 * r34687918;
double r34687933 = i;
double r34687934 = r34687917 + r34687933;
double r34687935 = 1.3333333333333333;
double r34687936 = r34687934 / r34687935;
double r34687937 = r34687936 * r34687920;
double r34687938 = cbrt(r34687937);
double r34687939 = 2.0;
double r34687940 = r34687938 / r34687939;
double r34687941 = r34687932 / r34687940;
double r34687942 = r34687930 - r34687941;
double r34687943 = r34687942 / r34687914;
double r34687944 = exp(r34687943);
double r34687945 = r34687929 / r34687944;
double r34687946 = Dvac;
double r34687947 = r34687945 * r34687946;
double r34687948 = cbrt(r34687934);
double r34687949 = r34687947 * r34687948;
double r34687950 = r34687923 / r34687920;
double r34687951 = cbrt(r34687950);
double r34687952 = r34687922 * r34687951;
double r34687953 = r34687946 * r34687952;
double r34687954 = r34687948 * r34687953;
double r34687955 = r34687916 ? r34687949 : r34687954;
return r34687955;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Split input into 2 regimes
2. ## if (* KB T) < 4.999127391294479e+286

1. Initial program 23.0

$\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{Vat}}{Vat}\right)}^{\left(\frac{1}{3}\right)} \cdot Dvac\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(EFvac - \frac{\left(2 \cdot Gama\right) \cdot Vat}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot Vat}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{KB \cdot T}}$
2. Simplified21.3

$\leadsto \color{blue}{\left(Dvac \cdot \frac{\sqrt[3]{\frac{48}{\frac{Vat}{\pi} \cdot \frac{Vat}{\pi}}}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}}$
3. Using strategy rm
4. Applied *-un-lft-identity21.3

$\leadsto \left(Dvac \cdot \frac{\sqrt[3]{\frac{\color{blue}{1 \cdot 48}}{\frac{Vat}{\pi} \cdot \frac{Vat}{\pi}}}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}$
5. Applied times-frac21.2

$\leadsto \left(Dvac \cdot \frac{\sqrt[3]{\color{blue}{\frac{1}{\frac{Vat}{\pi}} \cdot \frac{48}{\frac{Vat}{\pi}}}}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}$
6. Applied cbrt-prod3.5

$\leadsto \left(Dvac \cdot \frac{\color{blue}{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{48}{\frac{Vat}{\pi}}}}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}$
7. Using strategy rm
8. Applied div-inv3.5

$\leadsto \left(Dvac \cdot \frac{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{48}{\color{blue}{Vat \cdot \frac{1}{\pi}}}}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}$
9. Applied *-un-lft-identity3.5

$\leadsto \left(Dvac \cdot \frac{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{\color{blue}{1 \cdot 48}}{Vat \cdot \frac{1}{\pi}}}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}$
10. Applied times-frac3.5

$\leadsto \left(Dvac \cdot \frac{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\color{blue}{\frac{1}{Vat} \cdot \frac{48}{\frac{1}{\pi}}}}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}$
11. Applied cbrt-prod3.3

$\leadsto \left(Dvac \cdot \frac{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \color{blue}{\left(\sqrt[3]{\frac{1}{Vat}} \cdot \sqrt[3]{\frac{48}{\frac{1}{\pi}}}\right)}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}$
12. Simplified3.3

$\leadsto \left(Dvac \cdot \frac{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \left(\sqrt[3]{\frac{1}{Vat}} \cdot \color{blue}{\sqrt[3]{48 \cdot \pi}}\right)}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}$

## if 4.999127391294479e+286 < (* KB T)

1. Initial program 32.2

$\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{Vat}}{Vat}\right)}^{\left(\frac{1}{3}\right)} \cdot Dvac\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(EFvac - \frac{\left(2 \cdot Gama\right) \cdot Vat}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot Vat}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{KB \cdot T}}$
2. Simplified30.4

$\leadsto \color{blue}{\left(Dvac \cdot \frac{\sqrt[3]{\frac{48}{\frac{Vat}{\pi} \cdot \frac{Vat}{\pi}}}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}}$
3. Using strategy rm
4. Applied *-un-lft-identity30.4

$\leadsto \left(Dvac \cdot \frac{\sqrt[3]{\frac{\color{blue}{1 \cdot 48}}{\frac{Vat}{\pi} \cdot \frac{Vat}{\pi}}}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}$
5. Applied times-frac30.0

$\leadsto \left(Dvac \cdot \frac{\sqrt[3]{\color{blue}{\frac{1}{\frac{Vat}{\pi}} \cdot \frac{48}{\frac{Vat}{\pi}}}}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}$
6. Applied cbrt-prod9.8

$\leadsto \left(Dvac \cdot \frac{\color{blue}{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{48}{\frac{Vat}{\pi}}}}}{e^{\frac{EFvac - \frac{Vat \cdot Gama}{\frac{\sqrt[3]{\frac{i + 1}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{KB \cdot T}}}\right) \cdot \sqrt[3]{i + 1}$
7. Taylor expanded around inf 2.7

$\leadsto \left(Dvac \cdot \frac{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{48}{\frac{Vat}{\pi}}}}{e^{\color{blue}{0}}}\right) \cdot \sqrt[3]{i + 1}$
3. Recombined 2 regimes into one program.
4. Final simplification3.2

$\leadsto \begin{array}{l} \mathbf{if}\;T \cdot KB \le 4.999127391294479 \cdot 10^{+286}:\\ \;\;\;\;\left(\frac{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \left(\sqrt[3]{\pi \cdot 48} \cdot \sqrt[3]{\frac{1}{Vat}}\right)}{e^{\frac{EFvac - \frac{Gama \cdot Vat}{\frac{\sqrt[3]{\frac{1 + i}{\frac{4}{3}} \cdot \frac{Vat}{\pi}}}{2}}}{T \cdot KB}}} \cdot Dvac\right) \cdot \sqrt[3]{1 + i}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{1 + i} \cdot \left(Dvac \cdot \left(\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{48}{\frac{Vat}{\pi}}}\right)\right)\\ \end{array}$

# Reproduce

herbie shell --seed 1
(FPCore (Vat Dvac i EFvac Gama KB T)
:name "(pow((48*PI*PI/Vat/Vat),1/3)*Dvac)*pow((i+1),1/3)*exp(-(EFvac-2*Gama*Vat/pow((3*(i+1)*Vat/(4*PI)),1/3))/(KB*T))"
(* (* (* (pow (/ (/ (* (* 48 PI) PI) Vat) Vat) (/ 1 3)) Dvac) (pow (+ i 1) (/ 1 3))) (exp (/ (- (- EFvac (/ (* (* 2 Gama) Vat) (pow (/ (* (* 3 (+ i 1)) Vat) (* 4 PI)) (/ 1 3))))) (* KB T)))))