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

Average Error: 5.7 → 0.2

Time: 4.0s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r700801 = 1.0;
        double r700802 = x;
        double r700803 = r700801 - r700802;
        double r700804 = 3.0;
        double r700805 = r700804 - r700802;
        double r700806 = r700803 * r700805;
        double r700807 = y;
        double r700808 = r700807 * r700804;
        double r700809 = r700806 / r700808;
        return r700809;
}

↓

double f(double x, double y) {
        double r700810 = 1.0;
        double r700811 = x;
        double r700812 = r700810 - r700811;
        double r700813 = y;
        double r700814 = r700812 / r700813;
        double r700815 = 1.0;
        double r700816 = 3.0;
        double r700817 = r700816 - r700811;
        double r700818 = r700816 / r700817;
        double r700819 = r700815 / r700818;
        double r700820 = r700814 * r700819;
        return r700820;
}

Error

Bits error versus x

Bits error versus y

Target

Original	5.7
Target	0.1
Herbie	0.2

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

Derivation

1. Initial program 5.7

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

3. Applied times-frac 0.1

   \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}}\]
4. Using strategy rm

5. Applied clear-num 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1 x) y) (/ (- 3 x) 3))

  (/ (* (- 1 x) (- 3 x)) (* y 3)))