Average Error: 46.3 → 0.1
Time: 11.2s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}\]
\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}
↓
\frac{\frac{i}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}
double f(double i) {
        double r41788 = i;
        double r41789 = r41788 * r41788;
        double r41790 = r41789 * r41789;
        double r41791 = 2.0;
        double r41792 = r41791 * r41788;
        double r41793 = r41792 * r41792;
        double r41794 = r41790 / r41793;
        double r41795 = 1.0;
        double r41796 = r41793 - r41795;
        double r41797 = r41794 / r41796;
        return r41797;
}
↓
double f(double i) {
        double r41798 = i;
        double r41799 = 2.0;
        double r41800 = r41799 * r41799;
        double r41801 = r41798 / r41800;
        double r41802 = r41799 * r41798;
        double r41803 = r41799 * r41802;
        double r41804 = 1.0;
        double r41805 = r41804 / r41798;
        double r41806 = r41803 - r41805;
        double r41807 = r41801 / r41806;
        return r41807;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.3

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 
(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)))