Average Error: 6.9 → 0.2
Time: 32.4s
Precision: 64
$i \le 2500$
$\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}$
$\frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{\left(\sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}\right) \cdot \sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}} \cdot \frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{{\left(e^{\sqrt{\frac{1.77 - \frac{2 \cdot 1.205 \cdot 10^{-29}}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}\right)}^{\left(\sqrt{\frac{1.77 - \frac{2 \cdot 1.205 \cdot 10^{-29}}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}\right)}}$
\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}}{\left(\sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}\right) \cdot \sqrt[3]{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}}}}{{\left(e^{\sqrt{\frac{1.77 - \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}}}}\right)}^{\left(\sqrt{\frac{1.77 - \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}}}\right)}}
double f(double i) {
double r24811688 = 48.0;
double r24811689 = atan2(1.0, 0.0);
double r24811690 = r24811688 * r24811689;
double r24811691 = r24811690 * r24811689;
double r24811692 = 1.205e-29;
double r24811693 = r24811691 / r24811692;
double r24811694 = r24811693 / r24811692;
double r24811695 = 1.0;
double r24811696 = 3.0;
double r24811697 = r24811695 / r24811696;
double r24811698 = pow(r24811694, r24811697);
double r24811699 = 1e-06;
double r24811700 = 1.1;
double r24811701 = -r24811700;
double r24811702 = 8.625e-05;
double r24811703 = 823.0;
double r24811704 = r24811702 * r24811703;
double r24811705 = r24811701 / r24811704;
double r24811706 = exp(r24811705);
double r24811707 = r24811699 * r24811706;
double r24811708 = r24811698 * r24811707;
double r24811709 = i;
double r24811710 = r24811709 + r24811695;
double r24811711 = pow(r24811710, r24811697);
double r24811712 = r24811708 * r24811711;
double r24811713 = 1.77;
double r24811714 = 2.0;
double r24811715 = 6.25e+18;
double r24811716 = r24811714 * r24811715;
double r24811717 = r24811716 * r24811692;
double r24811718 = r24811696 * r24811710;
double r24811719 = r24811718 * r24811692;
double r24811720 = 4.0;
double r24811721 = r24811720 * r24811689;
double r24811722 = r24811719 / r24811721;
double r24811723 = pow(r24811722, r24811697);
double r24811724 = r24811717 / r24811723;
double r24811725 = r24811713 - r24811724;
double r24811726 = -r24811725;
double r24811727 = r24811726 / r24811704;
double r24811728 = exp(r24811727);
double r24811729 = r24811712 * r24811728;
return r24811729;
}


double f(double i) {
double r24811730 = 1.0;
double r24811731 = i;
double r24811732 = r24811730 + r24811731;
double r24811733 = cbrt(r24811732);
double r24811734 = 1e-06;
double r24811735 = r24811733 * r24811734;
double r24811736 = 1.1;
double r24811737 = 823.0;
double r24811738 = 8.625e-05;
double r24811739 = r24811737 * r24811738;
double r24811740 = r24811736 / r24811739;
double r24811741 = exp(r24811740);
double r24811742 = cbrt(r24811741);
double r24811743 = r24811742 * r24811742;
double r24811744 = r24811743 * r24811742;
double r24811745 = r24811735 / r24811744;
double r24811746 = atan2(1.0, 0.0);
double r24811747 = 1.205e-29;
double r24811748 = r24811746 / r24811747;
double r24811749 = 48.0;
double r24811750 = r24811748 * r24811749;
double r24811751 = r24811750 * r24811748;
double r24811752 = cbrt(r24811751);
double r24811753 = 1.77;
double r24811754 = 2.0;
double r24811755 = r24811754 * r24811747;
double r24811756 = 1.3333333333333333;
double r24811757 = r24811747 / r24811746;
double r24811758 = r24811756 / r24811757;
double r24811759 = r24811732 / r24811758;
double r24811760 = cbrt(r24811759);
double r24811761 = 6.25e+18;
double r24811762 = r24811760 / r24811761;
double r24811763 = r24811755 / r24811762;
double r24811764 = r24811753 - r24811763;
double r24811765 = r24811764 / r24811739;
double r24811766 = sqrt(r24811765);
double r24811767 = exp(r24811766);
double r24811768 = pow(r24811767, r24811766);
double r24811769 = r24811752 / r24811768;
double r24811770 = r24811745 * r24811769;
return r24811770;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 6.9

$\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}$
2. Simplified2.6

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

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

$\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{\left(\sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}\right) \cdot \sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}} \cdot \frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{e^{\color{blue}{\sqrt{\frac{1.77 - \frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}} \cdot \sqrt{\frac{1.77 - \frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}}$
7. Applied exp-prod0.2

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

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

# 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 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)))))