Average Error: 5.9 → 0.1
Time: 16.5s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \frac{1 - \frac{x}{3}}{y}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \frac{1 - \frac{x}{3}}{y}
double f(double x, double y) {
        double r411705 = 1.0;
        double r411706 = x;
        double r411707 = r411705 - r411706;
        double r411708 = 3.0;
        double r411709 = r411708 - r411706;
        double r411710 = r411707 * r411709;
        double r411711 = y;
        double r411712 = r411711 * r411708;
        double r411713 = r411710 / r411712;
        return r411713;
}
↓
double f(double x, double y) {
        double r411714 = 1.0;
        double r411715 = x;
        double r411716 = r411714 - r411715;
        double r411717 = 1.0;
        double r411718 = 3.0;
        double r411719 = r411715 / r411718;
        double r411720 = r411717 - r411719;
        double r411721 = y;
        double r411722 = r411720 / r411721;
        double r411723 = r411716 * r411722;
        return r411723;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

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

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

  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

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 +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)))