Average Error: 5.9 → 0.1
Time: 11.8s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{\frac{3 - x}{3}}{y} \cdot \left(1 - x\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{\frac{3 - x}{3}}{y} \cdot \left(1 - x\right)
double f(double x, double y) {
        double r33017804 = 1.0;
        double r33017805 = x;
        double r33017806 = r33017804 - r33017805;
        double r33017807 = 3.0;
        double r33017808 = r33017807 - r33017805;
        double r33017809 = r33017806 * r33017808;
        double r33017810 = y;
        double r33017811 = r33017810 * r33017807;
        double r33017812 = r33017809 / r33017811;
        return r33017812;
}
↓
double f(double x, double y) {
        double r33017813 = 3.0;
        double r33017814 = x;
        double r33017815 = r33017813 - r33017814;
        double r33017816 = r33017815 / r33017813;
        double r33017817 = y;
        double r33017818 = r33017816 / r33017817;
        double r33017819 = 1.0;
        double r33017820 = r33017819 - r33017814;
        double r33017821 = r33017818 * r33017820;
        return r33017821;
}

Error

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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

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))