Average Error: 5.7 → 0.2
Time: 15.2s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1}{\frac{y}{1 - x}} \cdot \left(1 - \frac{x}{3}\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1}{\frac{y}{1 - x}} \cdot \left(1 - \frac{x}{3}\right)
double f(double x, double y) {
        double r414654 = 1.0;
        double r414655 = x;
        double r414656 = r414654 - r414655;
        double r414657 = 3.0;
        double r414658 = r414657 - r414655;
        double r414659 = r414656 * r414658;
        double r414660 = y;
        double r414661 = r414660 * r414657;
        double r414662 = r414659 / r414661;
        return r414662;
}
↓
double f(double x, double y) {
        double r414663 = 1.0;
        double r414664 = y;
        double r414665 = 1.0;
        double r414666 = x;
        double r414667 = r414665 - r414666;
        double r414668 = r414664 / r414667;
        double r414669 = r414663 / r414668;
        double r414670 = 3.0;
        double r414671 = r414666 / r414670;
        double r414672 = r414663 - r414671;
        double r414673 = r414669 * r414672;
        return r414673;
}

Error

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Bits error versus y

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Results

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Target

Original5.7
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

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

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

  6. Simplified0.1

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

  8. Applied clear-num0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(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)))