Average Error: 5.3 → 0.1
Time: 16.9s
Precision: 64
\[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
↓
\[\frac{\frac{3.0 - x}{3.0}}{y} \cdot \left(1.0 - x\right)\]
\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}
↓
\frac{\frac{3.0 - x}{3.0}}{y} \cdot \left(1.0 - x\right)
double f(double x, double y) {
        double r30486849 = 1.0;
        double r30486850 = x;
        double r30486851 = r30486849 - r30486850;
        double r30486852 = 3.0;
        double r30486853 = r30486852 - r30486850;
        double r30486854 = r30486851 * r30486853;
        double r30486855 = y;
        double r30486856 = r30486855 * r30486852;
        double r30486857 = r30486854 / r30486856;
        return r30486857;
}
↓
double f(double x, double y) {
        double r30486858 = 3.0;
        double r30486859 = x;
        double r30486860 = r30486858 - r30486859;
        double r30486861 = r30486860 / r30486858;
        double r30486862 = y;
        double r30486863 = r30486861 / r30486862;
        double r30486864 = 1.0;
        double r30486865 = r30486864 - r30486859;
        double r30486866 = r30486863 * r30486865;
        return r30486866;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original5.3
Target0.1
Herbie0.1
\[\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}\]

Derivation

  1. Initial program 5.3

    \[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
  2. Using strategy rm

  3. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.1

    \[\leadsto \frac{1.0 - x}{y} \cdot \frac{3.0 - x}{\color{blue}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \sqrt[3]{3.0}}}\]

  6. Applied associate-/r*0.2

    \[\leadsto \frac{1.0 - x}{y} \cdot \color{blue}{\frac{\frac{3.0 - x}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}}}{\sqrt[3]{3.0}}}\]
  7. Using strategy rm

  8. Applied div-inv0.2

    \[\leadsto \color{blue}{\left(\left(1.0 - x\right) \cdot \frac{1}{y}\right)} \cdot \frac{\frac{3.0 - x}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}}}{\sqrt[3]{3.0}}\]

  9. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\left(1.0 - x\right) \cdot \left(\frac{1}{y} \cdot \frac{\frac{3.0 - x}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}}}{\sqrt[3]{3.0}}\right)}\]

  10. Simplified0.1

    \[\leadsto \left(1.0 - x\right) \cdot \color{blue}{\frac{\frac{3.0 - x}{3.0}}{y}}\]

  11. Final simplification0.1

    \[\leadsto \frac{\frac{3.0 - x}{3.0}}{y} \cdot \left(1.0 - x\right)\]

Reproduce

herbie shell --seed 2019164 +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)))