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

Average Error: 34.3 → 4.1

Time: 7.1s

Precision: binary64

Math

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

↓

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

C

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

↓

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	34.3
Target	0.4
Herbie	4.1

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

Derivation

1. Initial program 34.3

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

2. Simplified 25.4

   \[\leadsto \color{blue}{x \cdot \frac{x}{y \cdot y} + z \cdot \frac{z}{t \cdot t}}\]
3. Using strategy rm

4. Applied add-sqr-sqrt 44.6

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

5. Applied times-frac 40.6

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

6. Applied add-sqr-sqrt 40.7

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

7. Applied unswap-sqr 39.0

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

8. Simplified 38.9

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

9. Simplified 13.4

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

11. Applied clear-num 13.4

    \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y \cdot y}{x}}} + \frac{z}{t} \cdot \frac{z}{t}\]

12. Simplified 4.6

    \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot \frac{y}{x}}} + \frac{z}{t} \cdot \frac{z}{t}\]
13. Using strategy rm

14. Applied un-div-inv 4.1

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

15. Final simplification 4.1

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

Reproduce

herbie shell --seed 2020179 
(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) 2.0) (pow (/ z t) 2.0))

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