Average Error: 10.1 → 0.2
Time: 13.7s
Precision: 64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{\frac{x}{y}}{y}\]
\frac{x}{y \cdot y}
↓
\frac{\frac{x}{y}}{y}
double f(double x, double y) {
        double r14234190 = x;
        double r14234191 = y;
        double r14234192 = r14234191 * r14234191;
        double r14234193 = r14234190 / r14234192;
        return r14234193;
}
↓
double f(double x, double y) {
        double r14234194 = x;
        double r14234195 = y;
        double r14234196 = r14234194 / r14234195;
        double r14234197 = r14234196 / r14234195;
        return r14234197;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original10.1
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.1

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

  3. Applied associate-/r*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"

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

  (/ x (* y y)))