Average Error: 5.9 → 0.1
Time: 17.8s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \frac{\frac{3 - x}{3}}{y}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \frac{\frac{3 - x}{3}}{y}
double f(double x, double y) {
        double r500751 = 1.0;
        double r500752 = x;
        double r500753 = r500751 - r500752;
        double r500754 = 3.0;
        double r500755 = r500754 - r500752;
        double r500756 = r500753 * r500755;
        double r500757 = y;
        double r500758 = r500757 * r500754;
        double r500759 = r500756 / r500758;
        return r500759;
}
↓
double f(double x, double y) {
        double r500760 = 1.0;
        double r500761 = x;
        double r500762 = r500760 - r500761;
        double r500763 = 3.0;
        double r500764 = r500763 - r500761;
        double r500765 = r500764 / r500763;
        double r500766 = y;
        double r500767 = r500765 / r500766;
        double r500768 = r500762 * r500767;
        return r500768;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(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)))