Average Error: 45.5 → 0.4
Time: 16.2s
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 r3572760 = i;
        double r3572761 = r3572760 * r3572760;
        double r3572762 = r3572761 * r3572761;
        double r3572763 = 2.0;
        double r3572764 = r3572763 * r3572760;
        double r3572765 = r3572764 * r3572764;
        double r3572766 = r3572762 / r3572765;
        double r3572767 = 1.0;
        double r3572768 = r3572765 - r3572767;
        double r3572769 = r3572766 / r3572768;
        return r3572769;
}
↓
double f(double i) {
        double r3572770 = 0.25;
        double r3572771 = cbrt(r3572770);
        double r3572772 = r3572771 * r3572771;
        double r3572773 = 4.0;
        double r3572774 = 1.0;
        double r3572775 = i;
        double r3572776 = r3572775 * r3572775;
        double r3572777 = r3572774 / r3572776;
        double r3572778 = r3572773 - r3572777;
        double r3572779 = r3572771 / r3572778;
        double r3572780 = r3572772 * r3572779;
        return r3572780;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.5

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

  2. Simplified0.3

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

  4. Applied *-un-lft-identity0.3

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

  5. Applied add-cube-cbrt0.3

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

  6. Applied times-frac0.4

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

  7. Simplified0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019137 
(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)))