Average Error: 46.5 → 0.2
Time: 20.3s
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 r44984 = i;
        double r44985 = r44984 * r44984;
        double r44986 = r44985 * r44985;
        double r44987 = 2.0;
        double r44988 = r44987 * r44984;
        double r44989 = r44988 * r44988;
        double r44990 = r44986 / r44989;
        double r44991 = 1.0;
        double r44992 = r44989 - r44991;
        double r44993 = r44990 / r44992;
        return r44993;
}
↓
double f(double i) {
        double r44994 = i;
        double r44995 = 2.0;
        double r44996 = r44995 * r44995;
        double r44997 = r44994 / r44996;
        double r44998 = 1.0;
        double r44999 = r44995 * r44994;
        double r45000 = r44995 * r44999;
        double r45001 = 1.0;
        double r45002 = r45001 / r44994;
        double r45003 = r45000 - r45002;
        double r45004 = r44998 / r45003;
        double r45005 = r44997 * r45004;
        return r45005;
}

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)))