Average Error: 5.9 → 0.2
Time: 3.0s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \left(\left(3 - x\right) \cdot \frac{1}{3}\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \left(\left(3 - x\right) \cdot \frac{1}{3}\right)
double f(double x, double y) {
        double r596597 = 1.0;
        double r596598 = x;
        double r596599 = r596597 - r596598;
        double r596600 = 3.0;
        double r596601 = r596600 - r596598;
        double r596602 = r596599 * r596601;
        double r596603 = y;
        double r596604 = r596603 * r596600;
        double r596605 = r596602 / r596604;
        return r596605;
}
↓
double f(double x, double y) {
        double r596606 = 1.0;
        double r596607 = x;
        double r596608 = r596606 - r596607;
        double r596609 = y;
        double r596610 = r596608 / r596609;
        double r596611 = 3.0;
        double r596612 = r596611 - r596607;
        double r596613 = 1.0;
        double r596614 = r596613 / r596611;
        double r596615 = r596612 * r596614;
        double r596616 = r596610 * r596615;
        return r596616;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.9
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.9

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

  3. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

    \[\leadsto \frac{1 - x}{y} \cdot \color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{3}\right)}\]

  6. Final simplification0.2

    \[\leadsto \frac{1 - x}{y} \cdot \left(\left(3 - x\right) \cdot \frac{1}{3}\right)\]

Reproduce

herbie shell --seed 2019322 
(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)))