Average Error: 5.9 → 0.2
Time: 4.2s
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 r3891 = 1.0;
        double r3892 = x;
        double r3893 = r3891 - r3892;
        double r3894 = 3.0;
        double r3895 = r3894 - r3892;
        double r3896 = r3893 * r3895;
        double r3897 = y;
        double r3898 = r3897 * r3894;
        double r3899 = r3896 / r3898;
        return r3899;
}
↓
double f(double x, double y) {
        double r3900 = 1.0;
        double r3901 = x;
        double r3902 = r3900 - r3901;
        double r3903 = 1.0;
        double r3904 = y;
        double r3905 = r3903 / r3904;
        double r3906 = r3902 * r3905;
        double r3907 = 3.0;
        double r3908 = r3901 / r3907;
        double r3909 = r3903 - r3908;
        double r3910 = r3906 * r3909;
        return r3910;
}

Error

Bits error versus x

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 
(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)))