Average Error: 5.7 → 0.7
Time: 30.5s
Precision: 64
$i \gt 1$
$\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}$
$\frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\frac{\sqrt[3]{\left(48 \cdot \pi\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{2 \cdot 1.205 \cdot 10^{-29}}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}$
\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]{\left(48 \cdot \pi\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{2 \cdot 1.205 \cdot 10^{-29}}{\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 r29073564 = 48.0;
double r29073565 = atan2(1.0, 0.0);
double r29073566 = r29073564 * r29073565;
double r29073567 = r29073566 * r29073565;
double r29073568 = 1.205e-29;
double r29073569 = r29073567 / r29073568;
double r29073570 = r29073569 / r29073568;
double r29073571 = 1.0;
double r29073572 = 3.0;
double r29073573 = r29073571 / r29073572;
double r29073574 = pow(r29073570, r29073573);
double r29073575 = 1e-06;
double r29073576 = 1.1;
double r29073577 = -r29073576;
double r29073578 = 8.625e-05;
double r29073579 = 823.0;
double r29073580 = r29073578 * r29073579;
double r29073581 = r29073577 / r29073580;
double r29073582 = exp(r29073581);
double r29073583 = r29073575 * r29073582;
double r29073584 = r29073574 * r29073583;
double r29073585 = i;
double r29073586 = r29073585 + r29073571;
double r29073587 = pow(r29073586, r29073573);
double r29073588 = r29073584 * r29073587;
double r29073589 = 1.77;
double r29073590 = 2.0;
double r29073591 = 6.25e+18;
double r29073592 = r29073590 * r29073591;
double r29073593 = r29073592 * r29073568;
double r29073594 = r29073572 * r29073586;
double r29073595 = r29073594 * r29073568;
double r29073596 = 4.0;
double r29073597 = r29073596 * r29073565;
double r29073598 = r29073595 / r29073597;
double r29073599 = pow(r29073598, r29073573);
double r29073600 = r29073593 / r29073599;
double r29073601 = r29073589 - r29073600;
double r29073602 = -r29073601;
double r29073603 = r29073602 / r29073580;
double r29073604 = exp(r29073603);
double r29073605 = r29073588 * r29073604;
return r29073605;
}


double f(double i) {
double r29073606 = 1.0;
double r29073607 = i;
double r29073608 = r29073606 + r29073607;
double r29073609 = cbrt(r29073608);
double r29073610 = 1e-06;
double r29073611 = r29073609 * r29073610;
double r29073612 = 1.1;
double r29073613 = 823.0;
double r29073614 = 8.625e-05;
double r29073615 = r29073613 * r29073614;
double r29073616 = r29073612 / r29073615;
double r29073617 = exp(r29073616);
double r29073618 = r29073611 / r29073617;
double r29073619 = 48.0;
double r29073620 = atan2(1.0, 0.0);
double r29073621 = r29073619 * r29073620;
double r29073622 = 1.205e-29;
double r29073623 = r29073620 / r29073622;
double r29073624 = r29073621 * r29073623;
double r29073625 = cbrt(r29073624);
double r29073626 = cbrt(r29073622);
double r29073627 = r29073625 / r29073626;
double r29073628 = 1.77;
double r29073629 = r29073628 / r29073615;
double r29073630 = exp(r29073629);
double r29073631 = 2.0;
double r29073632 = r29073631 * r29073622;
double r29073633 = 1.3333333333333333;
double r29073634 = r29073622 / r29073620;
double r29073635 = r29073633 / r29073634;
double r29073636 = r29073608 / r29073635;
double r29073637 = cbrt(r29073636);
double r29073638 = 6.25e+18;
double r29073639 = r29073637 / r29073638;
double r29073640 = r29073632 / r29073639;
double r29073641 = r29073640 / r29073615;
double r29073642 = exp(r29073641);
double r29073643 = r29073630 / r29073642;
double r29073644 = r29073627 / r29073643;
double r29073645 = r29073618 * r29073644;
return r29073645;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 5.7

$\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}$
2. Simplified1.4

$\leadsto \color{blue}{\frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{e^{\frac{1.77 - \frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}$
3. Using strategy rm
4. Applied associate-*l/1.4

$\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\color{blue}{\frac{\pi \cdot 48}{1.205 \cdot 10^{-29}}} \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{e^{\frac{1.77 - \frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}$
5. Applied associate-*l/1.4

$\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\color{blue}{\frac{\left(\pi \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}}}}{e^{\frac{1.77 - \frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}$
6. Applied cbrt-div1.0

$\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\color{blue}{\frac{\sqrt[3]{\left(\pi \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}}{e^{\frac{1.77 - \frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}$
7. Using strategy rm
8. Applied div-sub0.9

$\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\frac{\sqrt[3]{\left(\pi \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}{e^{\color{blue}{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}} - \frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}$
9. Applied exp-diff0.7

$\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\frac{\sqrt[3]{\left(\pi \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}{\color{blue}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}}$
10. Final simplification0.7

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

# 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 (> i 1)
(* (* (* (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)))))