Average Error: 5.9 → 0.1
Time: 12.0s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{\frac{3 - x}{3}}{y} \cdot \left(1 - x\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{\frac{3 - x}{3}}{y} \cdot \left(1 - x\right)
double f(double x, double y) {
        double r31606920 = 1.0;
        double r31606921 = x;
        double r31606922 = r31606920 - r31606921;
        double r31606923 = 3.0;
        double r31606924 = r31606923 - r31606921;
        double r31606925 = r31606922 * r31606924;
        double r31606926 = y;
        double r31606927 = r31606926 * r31606923;
        double r31606928 = r31606925 / r31606927;
        return r31606928;
}
↓
double f(double x, double y) {
        double r31606929 = 3.0;
        double r31606930 = x;
        double r31606931 = r31606929 - r31606930;
        double r31606932 = r31606931 / r31606929;
        double r31606933 = y;
        double r31606934 = r31606932 / r31606933;
        double r31606935 = 1.0;
        double r31606936 = r31606935 - r31606930;
        double r31606937 = r31606934 * r31606936;
        return r31606937;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

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-inv0.2

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

  6. Applied associate-*l*0.2

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(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)))