Average Error: 5.9 → 0.2
Time: 4.6s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(\left(1 - x\right) \cdot \frac{1}{y}\right) \cdot \left(1 - \frac{x}{3}\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(\left(1 - x\right) \cdot \frac{1}{y}\right) \cdot \left(1 - \frac{x}{3}\right)
double f(double x, double y) {
        double r2654 = 1.0;
        double r2655 = x;
        double r2656 = r2654 - r2655;
        double r2657 = 3.0;
        double r2658 = r2657 - r2655;
        double r2659 = r2656 * r2658;
        double r2660 = y;
        double r2661 = r2660 * r2657;
        double r2662 = r2659 / r2661;
        return r2662;
}
↓
double f(double x, double y) {
        double r2663 = 1.0;
        double r2664 = x;
        double r2665 = r2663 - r2664;
        double r2666 = 1.0;
        double r2667 = y;
        double r2668 = r2666 / r2667;
        double r2669 = r2665 * r2668;
        double r2670 = 3.0;
        double r2671 = r2664 / r2670;
        double r2672 = r2666 - r2671;
        double r2673 = r2669 * r2672;
        return r2673;
}

Error

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Bits error versus y

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Results

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Target

Original5.9
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

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-sub0.1

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

  6. Simplified0.1

    \[\leadsto \frac{1 - x}{y} \cdot \left(\color{blue}{1} - \frac{x}{3}\right)\]
  7. Using strategy rm

  8. Applied div-inv0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020025 +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)))