Average Error: 9.9 → 0.2
Time: 12.0s
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 r171206 = x;
        double r171207 = y;
        double r171208 = r171207 * r171207;
        double r171209 = r171206 / r171208;
        return r171209;
}
↓
double f(double x, double y) {
        double r171210 = x;
        double r171211 = y;
        double r171212 = r171210 / r171211;
        double r171213 = r171212 / r171211;
        return r171213;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original9.9
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 9.9

    \[\frac{x}{y \cdot y}\]
  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 2019305 +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)))