Average Error: 5.7 → 0.1
Time: 3.2s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(\frac{1}{y} - \frac{x}{y}\right) \cdot \frac{3 - x}{3}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(\frac{1}{y} - \frac{x}{y}\right) \cdot \frac{3 - x}{3}
double f(double x, double y) {
        double r660590 = 1.0;
        double r660591 = x;
        double r660592 = r660590 - r660591;
        double r660593 = 3.0;
        double r660594 = r660593 - r660591;
        double r660595 = r660592 * r660594;
        double r660596 = y;
        double r660597 = r660596 * r660593;
        double r660598 = r660595 / r660597;
        return r660598;
}
↓
double f(double x, double y) {
        double r660599 = 1.0;
        double r660600 = y;
        double r660601 = r660599 / r660600;
        double r660602 = x;
        double r660603 = r660602 / r660600;
        double r660604 = r660601 - r660603;
        double r660605 = 3.0;
        double r660606 = r660605 - r660602;
        double r660607 = r660606 / r660605;
        double r660608 = r660604 * r660607;
        return r660608;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.7
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.7

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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-sub0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020049 
(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)))