Average Error: 5.5 → 0.2
Time: 19.2s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(\frac{1}{y} - \frac{1}{\frac{y}{\frac{x}{3}}}\right) \cdot \left(1 - x\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(\frac{1}{y} - \frac{1}{\frac{y}{\frac{x}{3}}}\right) \cdot \left(1 - x\right)
double f(double x, double y) {
        double r562629 = 1.0;
        double r562630 = x;
        double r562631 = r562629 - r562630;
        double r562632 = 3.0;
        double r562633 = r562632 - r562630;
        double r562634 = r562631 * r562633;
        double r562635 = y;
        double r562636 = r562635 * r562632;
        double r562637 = r562634 / r562636;
        return r562637;
}
↓
double f(double x, double y) {
        double r562638 = 1.0;
        double r562639 = y;
        double r562640 = r562638 / r562639;
        double r562641 = x;
        double r562642 = 3.0;
        double r562643 = r562641 / r562642;
        double r562644 = r562639 / r562643;
        double r562645 = r562638 / r562644;
        double r562646 = r562640 - r562645;
        double r562647 = 1.0;
        double r562648 = r562647 - r562641;
        double r562649 = r562646 * r562648;
        return r562649;
}

Error

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Bits error versus y

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Results

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Target

Original5.5
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.5

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

  2. Simplified0.4

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

  4. Applied div-sub0.4

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

  5. Simplified0.2

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

  6. Simplified0.2

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

  8. Applied clear-num0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019196 
(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)))