Average Error: 46.9 → 0.4
Time: 14.8s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{\left(2 \cdot 2 - \frac{1}{i \cdot i}\right) \cdot \left(2 \cdot 2\right)}\]
\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}
↓
\frac{1}{\left(2 \cdot 2 - \frac{1}{i \cdot i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r50693 = i;
        double r50694 = r50693 * r50693;
        double r50695 = r50694 * r50694;
        double r50696 = 2.0;
        double r50697 = r50696 * r50693;
        double r50698 = r50697 * r50697;
        double r50699 = r50695 / r50698;
        double r50700 = 1.0;
        double r50701 = r50698 - r50700;
        double r50702 = r50699 / r50701;
        return r50702;
}
↓
double f(double i) {
        double r50703 = 1.0;
        double r50704 = 2.0;
        double r50705 = r50704 * r50704;
        double r50706 = 1.0;
        double r50707 = i;
        double r50708 = r50707 * r50707;
        double r50709 = r50706 / r50708;
        double r50710 = r50705 - r50709;
        double r50711 = r50710 * r50705;
        double r50712 = r50703 / r50711;
        return r50712;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.9

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

  2. Simplified0.4

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

  3. Final simplification0.4

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(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)))