Average Error: 46.4 → 0.1
Time: 13.6s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}\]
\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{\frac{i}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}
double f(double i) {
        double r77835 = i;
        double r77836 = r77835 * r77835;
        double r77837 = r77836 * r77836;
        double r77838 = 2.0;
        double r77839 = r77838 * r77835;
        double r77840 = r77839 * r77839;
        double r77841 = r77837 / r77840;
        double r77842 = 1.0;
        double r77843 = r77840 - r77842;
        double r77844 = r77841 / r77843;
        return r77844;
}
↓
double f(double i) {
        double r77845 = i;
        double r77846 = 2.0;
        double r77847 = r77846 * r77846;
        double r77848 = r77845 / r77847;
        double r77849 = r77846 * r77845;
        double r77850 = r77846 * r77849;
        double r77851 = 1.0;
        double r77852 = r77851 / r77845;
        double r77853 = r77850 - r77852;
        double r77854 = r77848 / r77853;
        return r77854;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.4

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(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)))