Average Error: 46.7 → 0.0
Time: 13.2s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}} \cdot \frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}\]
\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}
↓
\frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}} \cdot \frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}
double f(double i) {
        double r2619966 = i;
        double r2619967 = r2619966 * r2619966;
        double r2619968 = r2619967 * r2619967;
        double r2619969 = 2.0;
        double r2619970 = r2619969 * r2619966;
        double r2619971 = r2619970 * r2619970;
        double r2619972 = r2619968 / r2619971;
        double r2619973 = 1.0;
        double r2619974 = r2619971 - r2619973;
        double r2619975 = r2619972 / r2619974;
        return r2619975;
}
↓
double f(double i) {
        double r2619976 = i;
        double r2619977 = 2.0;
        double r2619978 = r2619976 / r2619977;
        double r2619979 = r2619976 * r2619977;
        double r2619980 = 1.0;
        double r2619981 = sqrt(r2619980);
        double r2619982 = r2619979 - r2619981;
        double r2619983 = r2619978 / r2619982;
        double r2619984 = r2619979 + r2619981;
        double r2619985 = r2619978 / r2619984;
        double r2619986 = r2619983 * r2619985;
        return r2619986;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.7

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

  2. Simplified15.8

    \[\leadsto \color{blue}{\frac{\frac{i}{2} \cdot \frac{i}{2}}{\left(i \cdot 2\right) \cdot \left(i \cdot 2\right) - 1}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt15.8

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

  5. Applied difference-of-squares15.8

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

  6. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}} \cdot \frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}}}\]

  7. Final simplification0.0

    \[\leadsto \frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}} \cdot \frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}\]

Reproduce

herbie shell --seed 2019192 +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)))