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

Average Error: 33.8 → 0.4

Time: 5.5s

Precision: binary64

Cost: 960

Math

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

↓

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))

↓

(FPCore (x y z t)
 :precision binary64
 (+ (* (/ x y) (/ x y)) (* (/ z t) (/ z t))))

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	33.8
Target	0.4
Herbie	0.4

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

Alternatives

Alternative 1
Error	29.5
Cost	960

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

Alternative 2
Error	52.8
Cost	64

\[0\]

Alternative 3
Error	60.7
Cost	64

\[1\]

Derivation

1. Initial program 33.8

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

3. Applied times-frac_binary64_17475 19.4

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

5. Applied times-frac_binary64_17475 0.4

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

6. Simplified 0.4

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

7. Final simplification 0.4

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

Reproduce

herbie shell --seed 2021044 
(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))))