Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3

Average Error: 5.1 → 0.1

Time: 14.2s

Precision: 64

Math

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

↓

\[\frac{3.0 - x}{3.0} \cdot \frac{1.0 - x}{y}\]

C

double f(double x, double y) {
        double r26437633 = 1.0;
        double r26437634 = x;
        double r26437635 = r26437633 - r26437634;
        double r26437636 = 3.0;
        double r26437637 = r26437636 - r26437634;
        double r26437638 = r26437635 * r26437637;
        double r26437639 = y;
        double r26437640 = r26437639 * r26437636;
        double r26437641 = r26437638 / r26437640;
        return r26437641;
}

↓

double f(double x, double y) {
        double r26437642 = 3.0;
        double r26437643 = x;
        double r26437644 = r26437642 - r26437643;
        double r26437645 = r26437644 / r26437642;
        double r26437646 = 1.0;
        double r26437647 = r26437646 - r26437643;
        double r26437648 = y;
        double r26437649 = r26437647 / r26437648;
        double r26437650 = r26437645 * r26437649;
        return r26437650;
}

Error

Bits error versus x

Bits error versus y

Target

Original	5.1
Target	0.1
Herbie	0.1

\[\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}\]

Derivation

1. Initial program 5.1

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

3. Applied times-frac 0.1

   \[\leadsto \color{blue}{\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}}\]

4. Final simplification 0.1

   \[\leadsto \frac{3.0 - x}{3.0} \cdot \frac{1.0 - x}{y}\]

Reproduce

herbie shell --seed 2019158 +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)))