Average Error: 5.5 → 0.1
Time: 9.8s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \frac{3 - x}{3}
double f(double x, double y) {
        double r429754 = 1.0;
        double r429755 = x;
        double r429756 = r429754 - r429755;
        double r429757 = 3.0;
        double r429758 = r429757 - r429755;
        double r429759 = r429756 * r429758;
        double r429760 = y;
        double r429761 = r429760 * r429757;
        double r429762 = r429759 / r429761;
        return r429762;
}
↓
double f(double x, double y) {
        double r429763 = 1.0;
        double r429764 = x;
        double r429765 = r429763 - r429764;
        double r429766 = y;
        double r429767 = r429765 / r429766;
        double r429768 = 3.0;
        double r429769 = r429768 - r429764;
        double r429770 = r429769 / r429768;
        double r429771 = r429767 * r429770;
        return r429771;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.5

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

  3. Applied times-frac0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 
(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)))