Average Error: 5.8 → 0.1
Time: 2.8s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \frac{3 - x}{3}
double f(double x, double y) {
        double r725611 = 1.0;
        double r725612 = x;
        double r725613 = r725611 - r725612;
        double r725614 = 3.0;
        double r725615 = r725614 - r725612;
        double r725616 = r725613 * r725615;
        double r725617 = y;
        double r725618 = r725617 * r725614;
        double r725619 = r725616 / r725618;
        return r725619;
}
↓
double f(double x, double y) {
        double r725620 = 1.0;
        double r725621 = x;
        double r725622 = r725620 - r725621;
        double r725623 = y;
        double r725624 = r725622 / r725623;
        double r725625 = 3.0;
        double r725626 = r725625 - r725621;
        double r725627 = r725626 / r725625;
        double r725628 = r725624 * r725627;
        return r725628;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.8
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.8

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}}\]

  4. Final simplification0.1

    \[\leadsto \frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1 x) y) (/ (- 3 x) 3))

  (/ (* (- 1 x) (- 3 x)) (* y 3)))