Average Error: 45.7 → 0.5
Time: 36.1s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\left(\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}\right) \cdot \frac{\sqrt[3]{\frac{1}{4}}}{4 - \frac{1.0}{i \cdot i}}\]
\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}
↓
\left(\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}\right) \cdot \frac{\sqrt[3]{\frac{1}{4}}}{4 - \frac{1.0}{i \cdot i}}
double f(double i) {
        double r2938908 = i;
        double r2938909 = r2938908 * r2938908;
        double r2938910 = r2938909 * r2938909;
        double r2938911 = 2.0;
        double r2938912 = r2938911 * r2938908;
        double r2938913 = r2938912 * r2938912;
        double r2938914 = r2938910 / r2938913;
        double r2938915 = 1.0;
        double r2938916 = r2938913 - r2938915;
        double r2938917 = r2938914 / r2938916;
        return r2938917;
}
↓
double f(double i) {
        double r2938918 = 0.25;
        double r2938919 = cbrt(r2938918);
        double r2938920 = r2938919 * r2938919;
        double r2938921 = 4.0;
        double r2938922 = 1.0;
        double r2938923 = i;
        double r2938924 = r2938923 * r2938923;
        double r2938925 = r2938922 / r2938924;
        double r2938926 = r2938921 - r2938925;
        double r2938927 = r2938919 / r2938926;
        double r2938928 = r2938920 * r2938927;
        return r2938928;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.7

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]

  2. Simplified0.4

    \[\leadsto \color{blue}{\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.4

    \[\leadsto \frac{\frac{1}{4}}{\color{blue}{1 \cdot \left(4 - \frac{1.0}{i \cdot i}\right)}}\]

  5. Applied add-cube-cbrt0.4

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}\right) \cdot \sqrt[3]{\frac{1}{4}}}}{1 \cdot \left(4 - \frac{1.0}{i \cdot i}\right)}\]

  6. Applied times-frac0.5

    \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}}{1} \cdot \frac{\sqrt[3]{\frac{1}{4}}}{4 - \frac{1.0}{i \cdot i}}}\]

  7. Simplified0.5

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}\right)} \cdot \frac{\sqrt[3]{\frac{1}{4}}}{4 - \frac{1.0}{i \cdot i}}\]

  8. Final simplification0.5

    \[\leadsto \left(\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}\right) \cdot \frac{\sqrt[3]{\frac{1}{4}}}{4 - \frac{1.0}{i \cdot i}}\]

Reproduce

herbie shell --seed 2019146 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0)))