Average Error: 5.3 → 0.2
Time: 8.8s
Precision: 64
\[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
↓
\[\frac{3.0 - x}{3.0} \cdot \left(\left(1.0 - x\right) \cdot \frac{1}{y}\right)\]
\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}
↓
\frac{3.0 - x}{3.0} \cdot \left(\left(1.0 - x\right) \cdot \frac{1}{y}\right)
double f(double x, double y) {
        double r11365719 = 1.0;
        double r11365720 = x;
        double r11365721 = r11365719 - r11365720;
        double r11365722 = 3.0;
        double r11365723 = r11365722 - r11365720;
        double r11365724 = r11365721 * r11365723;
        double r11365725 = y;
        double r11365726 = r11365725 * r11365722;
        double r11365727 = r11365724 / r11365726;
        return r11365727;
}
↓
double f(double x, double y) {
        double r11365728 = 3.0;
        double r11365729 = x;
        double r11365730 = r11365728 - r11365729;
        double r11365731 = r11365730 / r11365728;
        double r11365732 = 1.0;
        double r11365733 = r11365732 - r11365729;
        double r11365734 = 1.0;
        double r11365735 = y;
        double r11365736 = r11365734 / r11365735;
        double r11365737 = r11365733 * r11365736;
        double r11365738 = r11365731 * r11365737;
        return r11365738;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.3
Target0.1
Herbie0.2
\[\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}\]

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 div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019156 +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)))