Average Error: 5.5 → 0.1
Time: 3.0s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \frac{\frac{3 - x}{3}}{y}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \frac{\frac{3 - x}{3}}{y}
double f(double x, double y) {
        double r726619 = 1.0;
        double r726620 = x;
        double r726621 = r726619 - r726620;
        double r726622 = 3.0;
        double r726623 = r726622 - r726620;
        double r726624 = r726621 * r726623;
        double r726625 = y;
        double r726626 = r726625 * r726622;
        double r726627 = r726624 / r726626;
        return r726627;
}
↓
double f(double x, double y) {
        double r726628 = 1.0;
        double r726629 = x;
        double r726630 = r726628 - r726629;
        double r726631 = 3.0;
        double r726632 = r726631 - r726629;
        double r726633 = r726632 / r726631;
        double r726634 = y;
        double r726635 = r726633 / r726634;
        double r726636 = r726630 * r726635;
        return r726636;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.5
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.5

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

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

  6. Applied associate-*l*0.2

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019356 
(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)))