Average Error: 6.9 → 0.2
Time: 30.6s
Precision: 64
$i \gt 0 \land i \lt 2500$
$\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}$
$\frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{\left(\sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}\right) \cdot \sqrt[3]{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}} \cdot \frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{{\left(e^{\sqrt{\frac{1.77 - \frac{2 \cdot 1.205 \cdot 10^{-29}}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}\right)}^{\left(\sqrt{\frac{1.77 - \frac{2 \cdot 1.205 \cdot 10^{-29}}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}\right)}}$
\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 r35992944 = 48.0;
double r35992945 = atan2(1.0, 0.0);
double r35992946 = r35992944 * r35992945;
double r35992947 = r35992946 * r35992945;
double r35992948 = 1.205e-29;
double r35992949 = r35992947 / r35992948;
double r35992950 = r35992949 / r35992948;
double r35992951 = 1.0;
double r35992952 = 3.0;
double r35992953 = r35992951 / r35992952;
double r35992954 = pow(r35992950, r35992953);
double r35992955 = 1e-06;
double r35992956 = 1.1;
double r35992957 = -r35992956;
double r35992958 = 8.625e-05;
double r35992959 = 823.0;
double r35992960 = r35992958 * r35992959;
double r35992961 = r35992957 / r35992960;
double r35992962 = exp(r35992961);
double r35992963 = r35992955 * r35992962;
double r35992964 = r35992954 * r35992963;
double r35992965 = i;
double r35992966 = r35992965 + r35992951;
double r35992967 = pow(r35992966, r35992953);
double r35992968 = r35992964 * r35992967;
double r35992969 = 1.77;
double r35992970 = 2.0;
double r35992971 = 6.25e+18;
double r35992972 = r35992970 * r35992971;
double r35992973 = r35992972 * r35992948;
double r35992974 = r35992952 * r35992966;
double r35992975 = r35992974 * r35992948;
double r35992976 = 4.0;
double r35992977 = r35992976 * r35992945;
double r35992978 = r35992975 / r35992977;
double r35992979 = pow(r35992978, r35992953);
double r35992980 = r35992973 / r35992979;
double r35992981 = r35992969 - r35992980;
double r35992982 = -r35992981;
double r35992983 = r35992982 / r35992960;
double r35992984 = exp(r35992983);
double r35992985 = r35992968 * r35992984;
return r35992985;
}


double f(double i) {
double r35992986 = 1.0;
double r35992987 = i;
double r35992988 = r35992986 + r35992987;
double r35992989 = cbrt(r35992988);
double r35992990 = 1e-06;
double r35992991 = r35992989 * r35992990;
double r35992992 = 1.1;
double r35992993 = 823.0;
double r35992994 = 8.625e-05;
double r35992995 = r35992993 * r35992994;
double r35992996 = r35992992 / r35992995;
double r35992997 = exp(r35992996);
double r35992998 = cbrt(r35992997);
double r35992999 = r35992998 * r35992998;
double r35993000 = r35992999 * r35992998;
double r35993001 = r35992991 / r35993000;
double r35993002 = atan2(1.0, 0.0);
double r35993003 = 1.205e-29;
double r35993004 = r35993002 / r35993003;
double r35993005 = 48.0;
double r35993006 = r35993004 * r35993005;
double r35993007 = r35993006 * r35993004;
double r35993008 = cbrt(r35993007);
double r35993009 = 1.77;
double r35993010 = 2.0;
double r35993011 = r35993010 * r35993003;
double r35993012 = 1.3333333333333333;
double r35993013 = r35993003 / r35993002;
double r35993014 = r35993012 / r35993013;
double r35993015 = r35992988 / r35993014;
double r35993016 = cbrt(r35993015);
double r35993017 = 6.25e+18;
double r35993018 = r35993016 / r35993017;
double r35993019 = r35993011 / r35993018;
double r35993020 = r35993009 - r35993019;
double r35993021 = r35993020 / r35992995;
double r35993022 = sqrt(r35993021);
double r35993023 = exp(r35993022);
double r35993024 = pow(r35993023, r35993022);
double r35993025 = r35993008 / r35993024;
double r35993026 = r35993001 * r35993025;
return r35993026;
}



# 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 (> i 0) (< 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)))))