Average Error: 10.7 → 0.2
Time: 4.0s
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 r420014 = x;
        double r420015 = y;
        double r420016 = r420015 * r420015;
        double r420017 = r420014 / r420016;
        return r420017;
}
↓
double f(double x, double y) {
        double r420018 = x;
        double r420019 = y;
        double r420020 = r420018 / r420019;
        double r420021 = r420020 / r420019;
        return r420021;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original10.7
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.7

    \[\frac{x}{y \cdot y}\]
  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 2020089 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))