Average Error: 6.0 → 0.1
Time: 3.4s
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 r727959 = 1.0;
        double r727960 = x;
        double r727961 = r727959 - r727960;
        double r727962 = 3.0;
        double r727963 = r727962 - r727960;
        double r727964 = r727961 * r727963;
        double r727965 = y;
        double r727966 = r727965 * r727962;
        double r727967 = r727964 / r727966;
        return r727967;
}
↓
double f(double x, double y) {
        double r727968 = 1.0;
        double r727969 = x;
        double r727970 = r727968 - r727969;
        double r727971 = 3.0;
        double r727972 = r727971 - r727969;
        double r727973 = r727972 / r727971;
        double r727974 = y;
        double r727975 = r727973 / r727974;
        double r727976 = r727970 * r727975;
        return r727976;
}

Error

Bits error versus x

Bits error versus y

Try it out

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Results

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Target

Original6.0
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 6.0

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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 2019353 +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)))