Average Error: 46.9 → 0.1
Time: 50.6s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2.0 \cdot i\right) \cdot \left(2.0 \cdot i\right)}}{\left(2.0 \cdot i\right) \cdot \left(2.0 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{i}{2.0 \cdot 2.0}}{i \cdot \left(2.0 \cdot 2.0\right) - \frac{1.0}{i}}\]
\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2.0 \cdot i\right) \cdot \left(2.0 \cdot i\right)}}{\left(2.0 \cdot i\right) \cdot \left(2.0 \cdot i\right) - 1.0}
↓
\frac{\frac{i}{2.0 \cdot 2.0}}{i \cdot \left(2.0 \cdot 2.0\right) - \frac{1.0}{i}}
double f(double i) {
        double r2568553 = i;
        double r2568554 = r2568553 * r2568553;
        double r2568555 = r2568554 * r2568554;
        double r2568556 = 2.0;
        double r2568557 = r2568556 * r2568553;
        double r2568558 = r2568557 * r2568557;
        double r2568559 = r2568555 / r2568558;
        double r2568560 = 1.0;
        double r2568561 = r2568558 - r2568560;
        double r2568562 = r2568559 / r2568561;
        return r2568562;
}
↓
double f(double i) {
        double r2568563 = i;
        double r2568564 = 2.0;
        double r2568565 = r2568564 * r2568564;
        double r2568566 = r2568563 / r2568565;
        double r2568567 = r2568563 * r2568565;
        double r2568568 = 1.0;
        double r2568569 = r2568568 / r2568563;
        double r2568570 = r2568567 - r2568569;
        double r2568571 = r2568566 / r2568570;
        return r2568571;
}

Error

Bits error versus i

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.9

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2.0 \cdot i\right) \cdot \left(2.0 \cdot i\right)}}{\left(2.0 \cdot i\right) \cdot \left(2.0 \cdot i\right) - 1.0}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{\frac{i}{2.0 \cdot 2.0}}{\left(2.0 \cdot 2.0\right) \cdot i - \frac{1.0}{i}}}\]

  3. Final simplification0.1

    \[\leadsto \frac{\frac{i}{2.0 \cdot 2.0}}{i \cdot \left(2.0 \cdot 2.0\right) - \frac{1.0}{i}}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i))) (- (* (* 2.0 i) (* 2.0 i)) 1.0)))