Average Error: 46.3 → 0.1
Time: 16.5s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2 \cdot 2}}{4 \cdot i - \frac{1}{i}}\]
\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 \cdot 2}}{4 \cdot i - \frac{1}{i}}
double f(double i) {
        double r80974 = i;
        double r80975 = r80974 * r80974;
        double r80976 = r80975 * r80975;
        double r80977 = 2.0;
        double r80978 = r80977 * r80974;
        double r80979 = r80978 * r80978;
        double r80980 = r80976 / r80979;
        double r80981 = 1.0;
        double r80982 = r80979 - r80981;
        double r80983 = r80980 / r80982;
        return r80983;
}
↓
double f(double i) {
        double r80984 = i;
        double r80985 = 2.0;
        double r80986 = r80985 * r80985;
        double r80987 = r80984 / r80986;
        double r80988 = 4.0;
        double r80989 = r80988 * r80984;
        double r80990 = 1.0;
        double r80991 = r80990 / r80984;
        double r80992 = r80989 - r80991;
        double r80993 = r80987 / r80992;
        return r80993;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.3

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

  2. Simplified0.1

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

  3. Taylor expanded around 0 0.1

    \[\leadsto \frac{\frac{i}{2 \cdot 2}}{\color{blue}{4 \cdot i - 1 \cdot \frac{1}{i}}}\]

  4. Simplified0.1

    \[\leadsto \frac{\frac{i}{2 \cdot 2}}{\color{blue}{4 \cdot i - \frac{1}{i}}}\]

  5. Final simplification0.1

    \[\leadsto \frac{\frac{i}{2 \cdot 2}}{4 \cdot i - \frac{1}{i}}\]

Reproduce

herbie shell --seed 2019351 
(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)))