Average Error: 47.1 → 0.2
Time: 6.7s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{\left(2 \cdot 2\right) \cdot \left(\left(2 \cdot 2\right) \cdot i - \frac{1}{i}\right)}\]
\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{i}{\left(2 \cdot 2\right) \cdot \left(\left(2 \cdot 2\right) \cdot i - \frac{1}{i}\right)}
double f(double i) {
        double r61928 = i;
        double r61929 = r61928 * r61928;
        double r61930 = r61929 * r61929;
        double r61931 = 2.0;
        double r61932 = r61931 * r61928;
        double r61933 = r61932 * r61932;
        double r61934 = r61930 / r61933;
        double r61935 = 1.0;
        double r61936 = r61933 - r61935;
        double r61937 = r61934 / r61936;
        return r61937;
}
↓
double f(double i) {
        double r61938 = i;
        double r61939 = 2.0;
        double r61940 = r61939 * r61939;
        double r61941 = r61940 * r61938;
        double r61942 = 1.0;
        double r61943 = r61942 / r61938;
        double r61944 = r61941 - r61943;
        double r61945 = r61940 * r61944;
        double r61946 = r61938 / r61945;
        return r61946;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 47.1

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(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)))