Average Error: 6.9 → 0.2
Time: 30.5s
Precision: 64
$0 \lt i \land i \lt 2500$
$\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}$
$\frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{\left(\sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}\right) \cdot \sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}} \cdot \frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{{\left(e^{\sqrt{\frac{1.77 - \frac{2 \cdot 1.205 \cdot 10^{-29}}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}\right)}^{\left(\sqrt{\frac{1.77 - \frac{2 \cdot 1.205 \cdot 10^{-29}}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}\right)}}$
\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 r22534790 = 48.0;
double r22534791 = atan2(1.0, 0.0);
double r22534792 = r22534790 * r22534791;
double r22534793 = r22534792 * r22534791;
double r22534794 = 1.205e-29;
double r22534795 = r22534793 / r22534794;
double r22534796 = r22534795 / r22534794;
double r22534797 = 1.0;
double r22534798 = 3.0;
double r22534799 = r22534797 / r22534798;
double r22534800 = pow(r22534796, r22534799);
double r22534801 = 1e-06;
double r22534802 = 1.1;
double r22534803 = -r22534802;
double r22534804 = 8.625e-05;
double r22534805 = 823.0;
double r22534806 = r22534804 * r22534805;
double r22534807 = r22534803 / r22534806;
double r22534808 = exp(r22534807);
double r22534809 = r22534801 * r22534808;
double r22534810 = r22534800 * r22534809;
double r22534811 = i;
double r22534812 = r22534811 + r22534797;
double r22534813 = pow(r22534812, r22534799);
double r22534814 = r22534810 * r22534813;
double r22534815 = 1.77;
double r22534816 = 2.0;
double r22534817 = 6.25e+18;
double r22534818 = r22534816 * r22534817;
double r22534819 = r22534818 * r22534794;
double r22534820 = r22534798 * r22534812;
double r22534821 = r22534820 * r22534794;
double r22534822 = 4.0;
double r22534823 = r22534822 * r22534791;
double r22534824 = r22534821 / r22534823;
double r22534825 = pow(r22534824, r22534799);
double r22534826 = r22534819 / r22534825;
double r22534827 = r22534815 - r22534826;
double r22534828 = -r22534827;
double r22534829 = r22534828 / r22534806;
double r22534830 = exp(r22534829);
double r22534831 = r22534814 * r22534830;
return r22534831;
}


double f(double i) {
double r22534832 = 1.0;
double r22534833 = i;
double r22534834 = r22534832 + r22534833;
double r22534835 = cbrt(r22534834);
double r22534836 = 1e-06;
double r22534837 = r22534835 * r22534836;
double r22534838 = 1.1;
double r22534839 = 823.0;
double r22534840 = 8.625e-05;
double r22534841 = r22534839 * r22534840;
double r22534842 = r22534838 / r22534841;
double r22534843 = exp(r22534842);
double r22534844 = cbrt(r22534843);
double r22534845 = r22534844 * r22534844;
double r22534846 = r22534845 * r22534844;
double r22534847 = r22534837 / r22534846;
double r22534848 = atan2(1.0, 0.0);
double r22534849 = 1.205e-29;
double r22534850 = r22534848 / r22534849;
double r22534851 = 48.0;
double r22534852 = r22534850 * r22534851;
double r22534853 = r22534852 * r22534850;
double r22534854 = cbrt(r22534853);
double r22534855 = 1.77;
double r22534856 = 2.0;
double r22534857 = r22534856 * r22534849;
double r22534858 = 1.3333333333333333;
double r22534859 = r22534849 / r22534848;
double r22534860 = r22534858 / r22534859;
double r22534861 = r22534834 / r22534860;
double r22534862 = cbrt(r22534861);
double r22534863 = 6.25e+18;
double r22534864 = r22534862 / r22534863;
double r22534865 = r22534857 / r22534864;
double r22534866 = r22534855 - r22534865;
double r22534867 = r22534866 / r22534841;
double r22534868 = sqrt(r22534867);
double r22534869 = exp(r22534868);
double r22534870 = pow(r22534869, r22534868);
double r22534871 = r22534854 / r22534870;
double r22534872 = r22534847 * r22534871;
return r22534872;
}



# 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 (and (< 0 i) (< 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)))))