Average Error: 10.6 → 0.2
Time: 2.1s
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 r270978 = x;
        double r270979 = y;
        double r270980 = r270979 * r270979;
        double r270981 = r270978 / r270980;
        return r270981;
}
↓
double f(double x, double y) {
        double r270982 = x;
        double r270983 = y;
        double r270984 = r270982 / r270983;
        double r270985 = r270984 / r270983;
        return r270985;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original10.6
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.6

    \[\frac{x}{y \cdot y}\]
  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 2020047 +o rules:numerics
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))