Average Error: 0.5 → 0.2
Time: 16.3s
Precision: 64
\[\frac{1.0}{x \cdot x}\]
↓
\[\frac{\frac{1.0}{x}}{x}\]
\frac{1.0}{x \cdot x}
↓
\frac{\frac{1.0}{x}}{x}
double f(double x) {
        double r21207762 = 1.0;
        double r21207763 = x;
        double r21207764 = r21207763 * r21207763;
        double r21207765 = r21207762 / r21207764;
        return r21207765;
}
↓
double f(double x) {
        double r21207766 = 1.0;
        double r21207767 = x;
        double r21207768 = r21207766 / r21207767;
        double r21207769 = r21207768 / r21207767;
        return r21207769;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.5
Target0.2
Herbie0.2
\[\frac{\frac{1.0}{x}}{x}\]

Derivation

  1. Initial program 0.5

    \[\frac{1.0}{x \cdot x}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{1.0}{x}}{x}}\]

  4. Final simplification0.2

    \[\leadsto \frac{\frac{1.0}{x}}{x}\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"

  :herbie-target
  (/ (/ 1.0 x) x)

  (/ 1.0 (* x x)))