Average Error: 46.5 → 0.2
Time: 19.7s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{2 \cdot 2} \cdot \frac{1}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}\]
\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{i}{2 \cdot 2} \cdot \frac{1}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}
double f(double i) {
        double r48979 = i;
        double r48980 = r48979 * r48979;
        double r48981 = r48980 * r48980;
        double r48982 = 2.0;
        double r48983 = r48982 * r48979;
        double r48984 = r48983 * r48983;
        double r48985 = r48981 / r48984;
        double r48986 = 1.0;
        double r48987 = r48984 - r48986;
        double r48988 = r48985 / r48987;
        return r48988;
}
↓
double f(double i) {
        double r48989 = i;
        double r48990 = 2.0;
        double r48991 = r48990 * r48990;
        double r48992 = r48989 / r48991;
        double r48993 = 1.0;
        double r48994 = r48990 * r48989;
        double r48995 = r48990 * r48994;
        double r48996 = 1.0;
        double r48997 = r48996 / r48989;
        double r48998 = r48995 - r48997;
        double r48999 = r48993 / r48998;
        double r49000 = r48992 * r48999;
        return r49000;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.5

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

  2. Simplified0.1

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

  4. Applied div-inv0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(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)))