Average Error: 5.5 → 1.8
Time: 31.6s
Precision: 64
$i \gt 1 \land i \lt 2500$
$\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}$
$\frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\frac{\sqrt[3]{\pi \cdot \left(48 \cdot \frac{\pi}{1.205 \cdot 10^{-29}}\right)}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}$
\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}
\frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\frac{\sqrt[3]{\pi \cdot \left(48 \cdot \frac{\pi}{1.205 \cdot 10^{-29}}\right)}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}
double f(double i) {
double r33580216 = 48.0;
double r33580217 = atan2(1.0, 0.0);
double r33580218 = r33580216 * r33580217;
double r33580219 = r33580218 * r33580217;
double r33580220 = 1.205e-29;
double r33580221 = r33580219 / r33580220;
double r33580222 = r33580221 / r33580220;
double r33580223 = 1.0;
double r33580224 = 3.0;
double r33580225 = r33580223 / r33580224;
double r33580226 = pow(r33580222, r33580225);
double r33580227 = 1e-06;
double r33580228 = 1.1;
double r33580229 = -r33580228;
double r33580230 = 8.625e-05;
double r33580231 = 823.0;
double r33580232 = r33580230 * r33580231;
double r33580233 = r33580229 / r33580232;
double r33580234 = exp(r33580233);
double r33580235 = r33580227 * r33580234;
double r33580236 = r33580226 * r33580235;
double r33580237 = i;
double r33580238 = r33580237 + r33580223;
double r33580239 = pow(r33580238, r33580225);
double r33580240 = r33580236 * r33580239;
double r33580241 = 1.77;
double r33580242 = 2.0;
double r33580243 = 6.25e+18;
double r33580244 = r33580242 * r33580243;
double r33580245 = r33580244 * r33580220;
double r33580246 = r33580224 * r33580238;
double r33580247 = r33580246 * r33580220;
double r33580248 = 4.0;
double r33580249 = r33580248 * r33580217;
double r33580250 = r33580247 / r33580249;
double r33580251 = pow(r33580250, r33580225);
double r33580252 = r33580245 / r33580251;
double r33580253 = r33580241 - r33580252;
double r33580254 = -r33580253;
double r33580255 = r33580254 / r33580232;
double r33580256 = exp(r33580255);
double r33580257 = r33580240 * r33580256;
return r33580257;
}


double f(double i) {
double r33580258 = 1.0;
double r33580259 = i;
double r33580260 = r33580258 + r33580259;
double r33580261 = cbrt(r33580260);
double r33580262 = 1e-06;
double r33580263 = r33580261 * r33580262;
double r33580264 = 1.1;
double r33580265 = 823.0;
double r33580266 = 8.625e-05;
double r33580267 = r33580265 * r33580266;
double r33580268 = r33580264 / r33580267;
double r33580269 = exp(r33580268);
double r33580270 = r33580263 / r33580269;
double r33580271 = atan2(1.0, 0.0);
double r33580272 = 48.0;
double r33580273 = 1.205e-29;
double r33580274 = r33580271 / r33580273;
double r33580275 = r33580272 * r33580274;
double r33580276 = r33580271 * r33580275;
double r33580277 = cbrt(r33580276);
double r33580278 = cbrt(r33580273);
double r33580279 = r33580277 / r33580278;
double r33580280 = 1.77;
double r33580281 = r33580280 / r33580267;
double r33580282 = exp(r33580281);
double r33580283 = 2.0;
double r33580284 = r33580273 * r33580283;
double r33580285 = 1.3333333333333333;
double r33580286 = r33580273 / r33580271;
double r33580287 = r33580285 / r33580286;
double r33580288 = r33580260 / r33580287;
double r33580289 = cbrt(r33580288);
double r33580290 = 6.25e+18;
double r33580291 = r33580289 / r33580290;
double r33580292 = r33580284 / r33580291;
double r33580293 = r33580292 / r33580267;
double r33580294 = exp(r33580293);
double r33580295 = r33580282 / r33580294;
double r33580296 = r33580279 / r33580295;
double r33580297 = r33580270 * r33580296;
return r33580297;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 5.5

$\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}$
2. Simplified2.8

$\leadsto \color{blue}{\frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{e^{\frac{1.77 - \frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}$
3. Using strategy rm
4. Applied div-sub2.6

$\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{e^{\color{blue}{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}} - \frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}$
5. Applied exp-diff1.9

$\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{\color{blue}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}}$
6. Using strategy rm
7. Applied associate-*r/1.9

$\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\color{blue}{\frac{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \pi}{1.205 \cdot 10^{-29}}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}$
8. Applied cbrt-div1.8

$\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\color{blue}{\frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \pi}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}$
9. Final simplification1.8

$\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\frac{\sqrt[3]{\pi \cdot \left(48 \cdot \frac{\pi}{1.205 \cdot 10^{-29}}\right)}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}$

# Reproduce

herbie shell --seed 1
(FPCore (i)
:name "(pow((48*PI*PI/1.205e-29/1.205e-29),1/3)*( 1.0e-6*exp(-1.1/(8.625e-5 * 823))))*pow((i+1),1/3)*exp(-(1.77-2* 6.25e18 *1.205e-29/(pow((3*(i+1)*1.205e-29/(4*PI)),1/3)))/( 8.625e-5 * 823))"
:pre (and (> i 1) (< i 2500))
(* (* (* (pow (/ (/ (* (* 48 PI) PI) 1.205e-29) 1.205e-29) (/ 1 3)) (* 1e-06 (exp (/ (- 1.1) (* 8.625e-05 823))))) (pow (+ i 1) (/ 1 3))) (exp (/ (- (- 1.77 (/ (* (* 2 6.25e+18) 1.205e-29) (pow (/ (* (* 3 (+ i 1)) 1.205e-29) (* 4 PI)) (/ 1 3))))) (* 8.625e-05 823)))))