Average Error: 10.5 → 0.2
Time: 2.0s
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 r305459 = x;
        double r305460 = y;
        double r305461 = r305460 * r305460;
        double r305462 = r305459 / r305461;
        return r305462;
}
↓
double f(double x, double y) {
        double r305463 = x;
        double r305464 = y;
        double r305465 = r305463 / r305464;
        double r305466 = r305465 / r305464;
        return r305466;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original10.5
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.5

    \[\frac{x}{y \cdot y}\]
  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 2020036 +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)))