Average Error: 46.6 → 0.3
Time: 8.8s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{1}{2}}{\left(2 \cdot 2 - \frac{1}{i \cdot i}\right) \cdot 2}\]
\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}
↓
\frac{\frac{1}{2}}{\left(2 \cdot 2 - \frac{1}{i \cdot i}\right) \cdot 2}
double f(double i) {
        double r75855 = i;
        double r75856 = r75855 * r75855;
        double r75857 = r75856 * r75856;
        double r75858 = 2.0;
        double r75859 = r75858 * r75855;
        double r75860 = r75859 * r75859;
        double r75861 = r75857 / r75860;
        double r75862 = 1.0;
        double r75863 = r75860 - r75862;
        double r75864 = r75861 / r75863;
        return r75864;
}
↓
double f(double i) {
        double r75865 = 1.0;
        double r75866 = 2.0;
        double r75867 = r75865 / r75866;
        double r75868 = r75866 * r75866;
        double r75869 = 1.0;
        double r75870 = i;
        double r75871 = r75870 * r75870;
        double r75872 = r75869 / r75871;
        double r75873 = r75868 - r75872;
        double r75874 = r75873 * r75866;
        double r75875 = r75867 / r75874;
        return r75875;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.6

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\left(2 \cdot 2 - \frac{1}{i \cdot i}\right) \cdot 2}}\]

  3. Final simplification0.3

    \[\leadsto \frac{\frac{1}{2}}{\left(2 \cdot 2 - \frac{1}{i \cdot i}\right) \cdot 2}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :precision binary64
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1)))