Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1

Average Error: 34.1 → 0.5

Time: 3.5s

Precision: 64

Math

\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]

↓

\[\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}} \cdot \left(\sqrt{\sqrt{\left|\frac{z}{t}\right|}} \cdot \sqrt{\sqrt{\left|\frac{z}{t}\right|}}\right)\]

C

double code(double x, double y, double z, double t) {
	return (((x * x) / (y * y)) + ((z * z) / (t * t)));
}

↓

double code(double x, double y, double z, double t) {
	return ((fabs((x / y)) * fabs((x / y))) + (pow(fabs((z / t)), 1.5) * (sqrt(sqrt(fabs((z / t)))) * sqrt(sqrt(fabs((z / t)))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	34.1
Target	0.4
Herbie	0.5

\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

1. Initial program 34.1

   \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
2. Using strategy rm

3. Applied add-sqr-sqrt 34.2

   \[\leadsto \color{blue}{\sqrt{\frac{x \cdot x}{y \cdot y}} \cdot \sqrt{\frac{x \cdot x}{y \cdot y}}} + \frac{z \cdot z}{t \cdot t}\]

4. Simplified 34.1

   \[\leadsto \color{blue}{\left|\frac{x}{y}\right|} \cdot \sqrt{\frac{x \cdot x}{y \cdot y}} + \frac{z \cdot z}{t \cdot t}\]

5. Simplified 19.7

   \[\leadsto \left|\frac{x}{y}\right| \cdot \color{blue}{\left|\frac{x}{y}\right|} + \frac{z \cdot z}{t \cdot t}\]
6. Using strategy rm

7. Applied add-sqr-sqrt 19.7

   \[\leadsto \left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \color{blue}{\sqrt{\frac{z \cdot z}{t \cdot t}} \cdot \sqrt{\frac{z \cdot z}{t \cdot t}}}\]

8. Simplified 19.7

   \[\leadsto \left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \color{blue}{\left|\frac{z}{t}\right|} \cdot \sqrt{\frac{z \cdot z}{t \cdot t}}\]

9. Simplified 0.4

   \[\leadsto \left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \left|\frac{z}{t}\right| \cdot \color{blue}{\left|\frac{z}{t}\right|}\]
10. Using strategy rm

11. Applied add-sqr-sqrt 0.5

    \[\leadsto \left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \left|\frac{z}{t}\right| \cdot \color{blue}{\left(\sqrt{\left|\frac{z}{t}\right|} \cdot \sqrt{\left|\frac{z}{t}\right|}\right)}\]

12. Applied associate-*r* 0.5

    \[\leadsto \left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \color{blue}{\left(\left|\frac{z}{t}\right| \cdot \sqrt{\left|\frac{z}{t}\right|}\right) \cdot \sqrt{\left|\frac{z}{t}\right|}}\]

13. Simplified 0.5

    \[\leadsto \left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \color{blue}{{\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}} \cdot \sqrt{\left|\frac{z}{t}\right|}\]
14. Using strategy rm

15. Applied add-sqr-sqrt 0.5

    \[\leadsto \left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\color{blue}{\sqrt{\left|\frac{z}{t}\right|} \cdot \sqrt{\left|\frac{z}{t}\right|}}}\]

16. Applied sqrt-prod 0.5

    \[\leadsto \left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}} \cdot \color{blue}{\left(\sqrt{\sqrt{\left|\frac{z}{t}\right|}} \cdot \sqrt{\sqrt{\left|\frac{z}{t}\right|}}\right)}\]

17. Final simplification 0.5

    \[\leadsto \left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}} \cdot \left(\sqrt{\sqrt{\left|\frac{z}{t}\right|}} \cdot \sqrt{\sqrt{\left|\frac{z}{t}\right|}}\right)\]

Reproduce

herbie shell --seed 2020058 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :herbie-target
  (+ (pow (/ x y) 2) (pow (/ z t) 2))

  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))