Average Error: 46.9 → 0.2
Time: 44.7s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2.0 \cdot i\right) \cdot \left(2.0 \cdot i\right)}}{\left(2.0 \cdot i\right) \cdot \left(2.0 \cdot i\right) - 1.0}\]
↓
\[\frac{i}{\left(i \cdot \left(2.0 \cdot 2.0\right) - \frac{1.0}{i}\right) \cdot \left(2.0 \cdot 2.0\right)}\]
\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{i}{\left(i \cdot \left(2.0 \cdot 2.0\right) - \frac{1.0}{i}\right) \cdot \left(2.0 \cdot 2.0\right)}
double f(double i) {
        double r2531176 = i;
        double r2531177 = r2531176 * r2531176;
        double r2531178 = r2531177 * r2531177;
        double r2531179 = 2.0;
        double r2531180 = r2531179 * r2531176;
        double r2531181 = r2531180 * r2531180;
        double r2531182 = r2531178 / r2531181;
        double r2531183 = 1.0;
        double r2531184 = r2531181 - r2531183;
        double r2531185 = r2531182 / r2531184;
        return r2531185;
}
↓
double f(double i) {
        double r2531186 = i;
        double r2531187 = 2.0;
        double r2531188 = r2531187 * r2531187;
        double r2531189 = r2531186 * r2531188;
        double r2531190 = 1.0;
        double r2531191 = r2531190 / r2531186;
        double r2531192 = r2531189 - r2531191;
        double r2531193 = r2531192 * r2531188;
        double r2531194 = r2531186 / r2531193;
        return r2531194;
}

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

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019165 
(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)))