Average Error: 45.6 → 0.2
Time: 12.7s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{i}{\left(i \cdot \left(2 \cdot 2\right) - \frac{1.0}{i}\right) \cdot \left(2 \cdot 2\right)}\]
\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}
↓
\frac{i}{\left(i \cdot \left(2 \cdot 2\right) - \frac{1.0}{i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r2780972 = i;
        double r2780973 = r2780972 * r2780972;
        double r2780974 = r2780973 * r2780973;
        double r2780975 = 2.0;
        double r2780976 = r2780975 * r2780972;
        double r2780977 = r2780976 * r2780976;
        double r2780978 = r2780974 / r2780977;
        double r2780979 = 1.0;
        double r2780980 = r2780977 - r2780979;
        double r2780981 = r2780978 / r2780980;
        return r2780981;
}
↓
double f(double i) {
        double r2780982 = i;
        double r2780983 = 2.0;
        double r2780984 = r2780983 * r2780983;
        double r2780985 = r2780982 * r2780984;
        double r2780986 = 1.0;
        double r2780987 = r2780986 / r2780982;
        double r2780988 = r2780985 - r2780987;
        double r2780989 = r2780988 * r2780984;
        double r2780990 = r2780982 / r2780989;
        return r2780990;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.6

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(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)))