Average Error: 10.0 → 0.2
Time: 6.2s
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 r242831 = x;
        double r242832 = y;
        double r242833 = r242832 * r242832;
        double r242834 = r242831 / r242833;
        return r242834;
}
↓
double f(double x, double y) {
        double r242835 = x;
        double r242836 = y;
        double r242837 = r242835 / r242836;
        double r242838 = r242837 / r242836;
        return r242838;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original10.0
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.0

    \[\frac{x}{y \cdot y}\]
  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 2019194 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"

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

  (/ x (* y y)))