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

Average Error: 33.3 → 0.3

Time: 3.4s

Precision: 64

Math

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

↓

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

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 (((x / y) / (y / x)) + ((z / t) / (t / z)));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	33.3
Target	0.4
Herbie	0.3

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

Derivation

1. Initial program 33.3

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

3. Applied times-frac 18.6

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

5. Applied times-frac 0.4

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

7. Applied clear-num 0.4

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

8. Applied un-div-inv 0.4

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

10. Applied clear-num 0.3

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

11. Applied un-div-inv 0.3

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

12. Final simplification 0.3

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

Reproduce

herbie shell --seed 2020078 
(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))))