Average Error: 46.3 → 0.3
Time: 11.8s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}\]
\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) - 1.0}
↓
\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}
double f(double i) {
        double r1827862 = i;
        double r1827863 = r1827862 * r1827862;
        double r1827864 = r1827863 * r1827863;
        double r1827865 = 2.0;
        double r1827866 = r1827865 * r1827862;
        double r1827867 = r1827866 * r1827866;
        double r1827868 = r1827864 / r1827867;
        double r1827869 = 1.0;
        double r1827870 = r1827867 - r1827869;
        double r1827871 = r1827868 / r1827870;
        return r1827871;
}
↓
double f(double i) {
        double r1827872 = 0.25;
        double r1827873 = 4.0;
        double r1827874 = 1.0;
        double r1827875 = i;
        double r1827876 = r1827875 * r1827875;
        double r1827877 = r1827874 / r1827876;
        double r1827878 = r1827873 - r1827877;
        double r1827879 = r1827872 / r1827878;
        return r1827879;
}

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

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}}\]

  3. Final simplification0.3

    \[\leadsto \frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}\]

Reproduce

herbie shell --seed 2019129 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0)))