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

Average Error: 5.5 → 0.1

Time: 5.6s

Precision: 64

Math

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

↓

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

C

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

↓

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

Error

Bits error versus x

Bits error versus y

Target

Original	5.5
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 5.5

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

3. Applied *-commutative 5.5

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

4. Applied *-commutative 5.5

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

5. Applied times-frac 0.1

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

7. Applied frac-2neg 0.1

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

8. Applied clear-num 0.2

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

9. Applied frac-times 0.1

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

10. Simplified 0.1

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

11. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020066 +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)))