Average Error: 26.0 → 1.7
Time: 1.9m
Precision: 64
• ## could not determine a ground truth for program body (more)

1. Vat = 4.0044935775862875e+107
2. EMvac = -268126401.37868768
3. KB = 1.886345247280214e-237
4. T = -1.1812213638920702e-101
5. i = -1.6163600377583066e-291
6. EFvac = -2.4988123859730367e-219
7. Gama = -3.390980731630323e+284
$\left(\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{Vat}}{Vat}\right)}^{\left(\frac{1}{3}\right)} \cdot 10^{-06}\right) \cdot e^{\frac{-EMvac}{KB \cdot T}}\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(EFvac - \frac{\left(2 \cdot Gama\right) \cdot Vat}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot Vat}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{KB \cdot T}}$
$\begin{array}{l} \mathbf{if}\;i \le 2.939496756689829 \cdot 10^{+69}:\\ \;\;\;\;\left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{2 \cdot Gama}{\frac{\sqrt[3]{\left(\frac{Vat}{\pi} \cdot \left(1 + i\right)\right) \cdot \frac{3}{4}}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right) \cdot \frac{\sqrt[3]{\frac{48}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{1}{\frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{\frac{\sqrt[3]{48} \cdot \sqrt[3]{48}}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{\sqrt[3]{48}}{\frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\sqrt[3]{1 + i} \cdot \frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{2 \cdot Gama}{\frac{\left(\frac{1}{3} \cdot \frac{e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log i + \log Vat\right)\right)\right)}}{\frac{i}{\sqrt[3]{\frac{3}{4}}}} + e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log i + \log Vat\right)\right)\right)} \cdot \sqrt[3]{\frac{3}{4}}\right) - \frac{\frac{1}{9}}{\frac{i \cdot i}{e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log i + \log Vat\right)\right)\right)} \cdot \sqrt[3]{\frac{3}{4}}}}}{Vat}}}{T}}{KB}}}\right)\\ \end{array}$
\left(\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{Vat}}{Vat}\right)}^{\left(\frac{1}{3}\right)} \cdot 10^{-06}\right) \cdot e^{\frac{-EMvac}{KB \cdot T}}\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}\;i \le 2.939496756689829 \cdot 10^{+69}:\\
\;\;\;\;\left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{2 \cdot Gama}{\frac{\sqrt[3]{\left(\frac{Vat}{\pi} \cdot \left(1 + i\right)\right) \cdot \frac{3}{4}}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right) \cdot \frac{\sqrt[3]{\frac{48}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{1}{\frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt[3]{\frac{\sqrt[3]{48} \cdot \sqrt[3]{48}}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{\sqrt[3]{48}}{\frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\sqrt[3]{1 + i} \cdot \frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{2 \cdot Gama}{\frac{\left(\frac{1}{3} \cdot \frac{e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log i + \log Vat\right)\right)\right)}}{\frac{i}{\sqrt[3]{\frac{3}{4}}}} + e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log i + \log Vat\right)\right)\right)} \cdot \sqrt[3]{\frac{3}{4}}\right) - \frac{\frac{1}{9}}{\frac{i \cdot i}{e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log i + \log Vat\right)\right)\right)} \cdot \sqrt[3]{\frac{3}{4}}}}}{Vat}}}{T}}{KB}}}\right)\\

\end{array}
double f(double Vat, double EMvac, double KB, double T, double i, double EFvac, double Gama) {
double r35811189 = 48.0;
double r35811190 = atan2(1.0, 0.0);
double r35811191 = r35811189 * r35811190;
double r35811192 = r35811191 * r35811190;
double r35811193 = Vat;
double r35811194 = r35811192 / r35811193;
double r35811195 = r35811194 / r35811193;
double r35811196 = 1.0;
double r35811197 = 3.0;
double r35811198 = r35811196 / r35811197;
double r35811199 = pow(r35811195, r35811198);
double r35811200 = 1e-06;
double r35811201 = r35811199 * r35811200;
double r35811202 = EMvac;
double r35811203 = -r35811202;
double r35811204 = KB;
double r35811205 = T;
double r35811206 = r35811204 * r35811205;
double r35811207 = r35811203 / r35811206;
double r35811208 = exp(r35811207);
double r35811209 = r35811201 * r35811208;
double r35811210 = i;
double r35811211 = r35811210 + r35811196;
double r35811212 = pow(r35811211, r35811198);
double r35811213 = r35811209 * r35811212;
double r35811214 = EFvac;
double r35811215 = 2.0;
double r35811216 = Gama;
double r35811217 = r35811215 * r35811216;
double r35811218 = r35811217 * r35811193;
double r35811219 = r35811197 * r35811211;
double r35811220 = r35811219 * r35811193;
double r35811221 = 4.0;
double r35811222 = r35811221 * r35811190;
double r35811223 = r35811220 / r35811222;
double r35811224 = pow(r35811223, r35811198);
double r35811225 = r35811218 / r35811224;
double r35811226 = r35811214 - r35811225;
double r35811227 = -r35811226;
double r35811228 = r35811227 / r35811206;
double r35811229 = exp(r35811228);
double r35811230 = r35811213 * r35811229;
return r35811230;
}

double f(double Vat, double EMvac, double KB, double T, double i, double EFvac, double Gama) {
double r35811231 = i;
double r35811232 = 2.939496756689829e+69;
bool r35811233 = r35811231 <= r35811232;
double r35811234 = 1e-06;
double r35811235 = EFvac;
double r35811236 = 2.0;
double r35811237 = Gama;
double r35811238 = r35811236 * r35811237;
double r35811239 = Vat;
double r35811240 = atan2(1.0, 0.0);
double r35811241 = r35811239 / r35811240;
double r35811242 = 1.0;
double r35811243 = r35811242 + r35811231;
double r35811244 = r35811241 * r35811243;
double r35811245 = 0.75;
double r35811246 = r35811244 * r35811245;
double r35811247 = cbrt(r35811246);
double r35811248 = r35811247 / r35811239;
double r35811249 = r35811238 / r35811248;
double r35811250 = r35811235 - r35811249;
double r35811251 = T;
double r35811252 = r35811250 / r35811251;
double r35811253 = KB;
double r35811254 = r35811252 / r35811253;
double r35811255 = exp(r35811254);
double r35811256 = r35811234 / r35811255;
double r35811257 = cbrt(r35811243);
double r35811258 = r35811256 * r35811257;
double r35811259 = 48.0;
double r35811260 = r35811259 / r35811241;
double r35811261 = cbrt(r35811260);
double r35811262 = r35811242 / r35811241;
double r35811263 = cbrt(r35811262);
double r35811264 = r35811261 * r35811263;
double r35811265 = EMvac;
double r35811266 = r35811265 / r35811253;
double r35811267 = r35811266 / r35811251;
double r35811268 = exp(r35811267);
double r35811269 = r35811264 / r35811268;
double r35811270 = r35811258 * r35811269;
double r35811271 = cbrt(r35811259);
double r35811272 = r35811271 * r35811271;
double r35811273 = r35811272 / r35811241;
double r35811274 = cbrt(r35811273);
double r35811275 = r35811271 / r35811241;
double r35811276 = cbrt(r35811275);
double r35811277 = r35811274 * r35811276;
double r35811278 = r35811277 / r35811268;
double r35811279 = 0.3333333333333333;
double r35811280 = log(r35811240);
double r35811281 = -r35811280;
double r35811282 = log(r35811231);
double r35811283 = log(r35811239);
double r35811284 = r35811282 + r35811283;
double r35811285 = -r35811284;
double r35811286 = r35811281 - r35811285;
double r35811287 = r35811279 * r35811286;
double r35811288 = exp(r35811287);
double r35811289 = cbrt(r35811245);
double r35811290 = r35811231 / r35811289;
double r35811291 = r35811288 / r35811290;
double r35811292 = r35811279 * r35811291;
double r35811293 = r35811288 * r35811289;
double r35811294 = r35811292 + r35811293;
double r35811295 = 0.1111111111111111;
double r35811296 = r35811231 * r35811231;
double r35811297 = r35811296 / r35811293;
double r35811298 = r35811295 / r35811297;
double r35811299 = r35811294 - r35811298;
double r35811300 = r35811299 / r35811239;
double r35811301 = r35811238 / r35811300;
double r35811302 = r35811235 - r35811301;
double r35811303 = r35811302 / r35811251;
double r35811304 = r35811303 / r35811253;
double r35811305 = exp(r35811304);
double r35811306 = r35811234 / r35811305;
double r35811307 = r35811257 * r35811306;
double r35811308 = r35811278 * r35811307;
double r35811309 = r35811233 ? r35811270 : r35811308;
return r35811309;
}

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Split input into 2 regimes
2. ## if i < 2.939496756689829e+69

1. Initial program 24.9

$\left(\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{Vat}}{Vat}\right)}^{\left(\frac{1}{3}\right)} \cdot 10^{-06}\right) \cdot e^{\frac{-EMvac}{KB \cdot T}}\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(EFvac - \frac{\left(2 \cdot Gama\right) \cdot Vat}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot Vat}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{KB \cdot T}}$
2. Simplified23.5

$\leadsto \color{blue}{\frac{\sqrt[3]{\frac{48}{\frac{Vat}{\pi} \cdot \frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{Gama \cdot 2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{Vat}{\pi}\right)}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right)}$
3. Using strategy rm
4. Applied *-un-lft-identity23.5

$\leadsto \frac{\sqrt[3]{\frac{\color{blue}{1 \cdot 48}}{\frac{Vat}{\pi} \cdot \frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{Gama \cdot 2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{Vat}{\pi}\right)}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right)$
5. Applied times-frac23.2

$\leadsto \frac{\sqrt[3]{\color{blue}{\frac{1}{\frac{Vat}{\pi}} \cdot \frac{48}{\frac{Vat}{\pi}}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{Gama \cdot 2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{Vat}{\pi}\right)}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right)$
6. Applied cbrt-prod1.9

$\leadsto \frac{\color{blue}{\sqrt[3]{\frac{1}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{48}{\frac{Vat}{\pi}}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{Gama \cdot 2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{Vat}{\pi}\right)}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right)$

## if 2.939496756689829e+69 < i

1. Initial program 29.1

$\left(\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{Vat}}{Vat}\right)}^{\left(\frac{1}{3}\right)} \cdot 10^{-06}\right) \cdot e^{\frac{-EMvac}{KB \cdot T}}\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(EFvac - \frac{\left(2 \cdot Gama\right) \cdot Vat}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot Vat}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{KB \cdot T}}$
2. Simplified24.8

$\leadsto \color{blue}{\frac{\sqrt[3]{\frac{48}{\frac{Vat}{\pi} \cdot \frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{Gama \cdot 2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{Vat}{\pi}\right)}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right)}$
3. Using strategy rm

$\leadsto \frac{\sqrt[3]{\frac{\color{blue}{\left(\sqrt[3]{48} \cdot \sqrt[3]{48}\right) \cdot \sqrt[3]{48}}}{\frac{Vat}{\pi} \cdot \frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{Gama \cdot 2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{Vat}{\pi}\right)}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right)$
5. Applied times-frac24.6

$\leadsto \frac{\sqrt[3]{\color{blue}{\frac{\sqrt[3]{48} \cdot \sqrt[3]{48}}{\frac{Vat}{\pi}} \cdot \frac{\sqrt[3]{48}}{\frac{Vat}{\pi}}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{Gama \cdot 2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{Vat}{\pi}\right)}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right)$
6. Applied cbrt-prod4.1

$\leadsto \frac{\color{blue}{\sqrt[3]{\frac{\sqrt[3]{48} \cdot \sqrt[3]{48}}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{\sqrt[3]{48}}{\frac{Vat}{\pi}}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{Gama \cdot 2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{Vat}{\pi}\right)}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right)$
7. Taylor expanded around inf 1.2

$\leadsto \frac{\sqrt[3]{\frac{\sqrt[3]{48} \cdot \sqrt[3]{48}}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{\sqrt[3]{48}}{\frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{Gama \cdot 2}{\frac{\color{blue}{\left(e^{\frac{1}{3} \cdot \left(\log \left(\frac{1}{\pi}\right) - \left(\log \left(\frac{1}{i}\right) + \log \left(\frac{1}{Vat}\right)\right)\right)} \cdot \sqrt[3]{\frac{3}{4}} + \frac{1}{3} \cdot \frac{e^{\frac{1}{3} \cdot \left(\log \left(\frac{1}{\pi}\right) - \left(\log \left(\frac{1}{i}\right) + \log \left(\frac{1}{Vat}\right)\right)\right)} \cdot \sqrt[3]{\frac{3}{4}}}{i}\right) - \frac{1}{9} \cdot \frac{e^{\frac{1}{3} \cdot \left(\log \left(\frac{1}{\pi}\right) - \left(\log \left(\frac{1}{i}\right) + \log \left(\frac{1}{Vat}\right)\right)\right)} \cdot \sqrt[3]{\frac{3}{4}}}{{i}^{2}}}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right)$
8. Simplified1.2

$\leadsto \frac{\sqrt[3]{\frac{\sqrt[3]{48} \cdot \sqrt[3]{48}}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{\sqrt[3]{48}}{\frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{Gama \cdot 2}{\frac{\color{blue}{\left(\sqrt[3]{\frac{3}{4}} \cdot e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log Vat + \log i\right)\right)\right)} + \frac{1}{3} \cdot \frac{e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log Vat + \log i\right)\right)\right)}}{\frac{i}{\sqrt[3]{\frac{3}{4}}}}\right) - \frac{\frac{1}{9}}{\frac{i \cdot i}{\sqrt[3]{\frac{3}{4}} \cdot e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log Vat + \log i\right)\right)\right)}}}}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right)$
3. Recombined 2 regimes into one program.
4. Final simplification1.7

$\leadsto \begin{array}{l} \mathbf{if}\;i \le 2.939496756689829 \cdot 10^{+69}:\\ \;\;\;\;\left(\frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{2 \cdot Gama}{\frac{\sqrt[3]{\left(\frac{Vat}{\pi} \cdot \left(1 + i\right)\right) \cdot \frac{3}{4}}}{Vat}}}{T}}{KB}}} \cdot \sqrt[3]{1 + i}\right) \cdot \frac{\sqrt[3]{\frac{48}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{1}{\frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{\frac{\sqrt[3]{48} \cdot \sqrt[3]{48}}{\frac{Vat}{\pi}}} \cdot \sqrt[3]{\frac{\sqrt[3]{48}}{\frac{Vat}{\pi}}}}{e^{\frac{\frac{EMvac}{KB}}{T}}} \cdot \left(\sqrt[3]{1 + i} \cdot \frac{10^{-06}}{e^{\frac{\frac{EFvac - \frac{2 \cdot Gama}{\frac{\left(\frac{1}{3} \cdot \frac{e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log i + \log Vat\right)\right)\right)}}{\frac{i}{\sqrt[3]{\frac{3}{4}}}} + e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log i + \log Vat\right)\right)\right)} \cdot \sqrt[3]{\frac{3}{4}}\right) - \frac{\frac{1}{9}}{\frac{i \cdot i}{e^{\frac{1}{3} \cdot \left(\left(-\log \pi\right) - \left(-\left(\log i + \log Vat\right)\right)\right)} \cdot \sqrt[3]{\frac{3}{4}}}}}{Vat}}}{T}}{KB}}}\right)\\ \end{array}$

# Reproduce

herbie shell --seed 1
(FPCore (Vat EMvac KB T i EFvac Gama)
:name "(pow((48*PI*PI/Vat/Vat),1/3)* 1.0e-6*exp(-EMvac/(KB*T)))*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)) 1e-06) (exp (/ (- EMvac) (* KB T)))) (pow (+ i 1) (/ 1 3))) (exp (/ (- (- EFvac (/ (* (* 2 Gama) Vat) (pow (/ (* (* 3 (+ i 1)) Vat) (* 4 PI)) (/ 1 3))))) (* KB T)))))