Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1

Average Error: 0.0 → 0.0

Time: 6.7s

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\frac{x - y}{z - y}\]

↓

\[\frac{x}{z - y} - \frac{y}{z - y}\]

C

double code(double x, double y, double z) {
	return (((double) (x - y)) / ((double) (z - y)));
}

↓

double code(double x, double y, double z) {
	return ((double) ((x / ((double) (z - y))) - (y / ((double) (z - y)))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\frac{x}{z - y} - \frac{y}{z - y}\]

Derivation

1. Initial program 0.0

   \[\frac{x - y}{z - y}\]
2. Using strategy rm

3. Applied div-sub 0.0

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

4. Final simplification 0.0

   \[\leadsto \frac{x}{z - y} - \frac{y}{z - y}\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (- (/ x (- z y)) (/ y (- z y)))

  (/ (- x y) (- z y)))