Average Error: 5.6 → 0.1
Time: 16.5s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{\frac{3 - x}{3}}{\frac{y}{1 - x}}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{\frac{3 - x}{3}}{\frac{y}{1 - x}}
double f(double x, double y) {
        double r498879 = 1.0;
        double r498880 = x;
        double r498881 = r498879 - r498880;
        double r498882 = 3.0;
        double r498883 = r498882 - r498880;
        double r498884 = r498881 * r498883;
        double r498885 = y;
        double r498886 = r498885 * r498882;
        double r498887 = r498884 / r498886;
        return r498887;
}
↓
double f(double x, double y) {
        double r498888 = 3.0;
        double r498889 = x;
        double r498890 = r498888 - r498889;
        double r498891 = r498890 / r498888;
        double r498892 = y;
        double r498893 = 1.0;
        double r498894 = r498893 - r498889;
        double r498895 = r498892 / r498894;
        double r498896 = r498891 / r498895;
        return r498896;
}

Error

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Results

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Target

Original5.6
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.6

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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 clear-num0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{1 - x}}} \cdot \frac{3 - x}{3}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity0.2

    \[\leadsto \frac{1}{\color{blue}{1 \cdot \frac{y}{1 - x}}} \cdot \frac{3 - x}{3}\]

  8. Applied add-sqr-sqrt0.2

    \[\leadsto \frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{1 \cdot \frac{y}{1 - x}} \cdot \frac{3 - x}{3}\]

  9. Applied times-frac0.2

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

  10. Applied associate-*l*0.2

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

  11. Simplified0.1

    \[\leadsto \frac{\sqrt{1}}{1} \cdot \color{blue}{\frac{\frac{3 - x}{3}}{\frac{y}{1 - x}}}\]

  12. Final simplification0.1

    \[\leadsto \frac{\frac{3 - x}{3}}{\frac{y}{1 - x}}\]

Reproduce

herbie shell --seed 2019323 
(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)))