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

Average Error: 5.4 → 0.1

Time: 17.4s

Precision: 64

Math

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

↓

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

C

double code(double x, double y) {
	return ((double) (((double) (((double) (1.0 - x)) * ((double) (3.0 - x)))) / ((double) (y * 3.0))));
}

↓

double code(double x, double y) {
	return ((double) (((double) (((double) (1.0 - x)) * 1.0)) / ((double) (y * ((double) (3.0 / ((double) (3.0 - x))))))));
}

Error

Bits error versus x

Bits error versus y

Target

Original	5.4
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 5.4

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

3. Applied *-un-lft-identity 5.4

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

4. Applied associate-*r* 5.4

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

5. Applied associate-/l* 0.3

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

7. Applied *-un-lft-identity 0.3

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

8. Applied times-frac 0.1

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

9. Simplified 0.1

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

10. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020113 +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)))