Average Error: 0.0 → 0.1
Time: 1.9s
Precision: 64
\[\frac{x - y}{z - y}\]
↓
\[\frac{x}{z - y} - y \cdot \frac{1}{z - y}\]
\frac{x - y}{z - y}
↓
\frac{x}{z - y} - y \cdot \frac{1}{z - y}
double code(double x, double y, double z) {
	return ((x - y) / (z - y));
}
↓
double code(double x, double y, double z) {
	return ((x / (z - y)) - (y * (1.0 / (z - y))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.1
\[\frac{x}{z - y} - \frac{y}{z - y}\]

Derivation

  1. Initial program 0.0

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

  3. Applied div-sub0.0

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

  5. Applied div-inv0.1

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

  6. Final simplification0.1

    \[\leadsto \frac{x}{z - y} - y \cdot \frac{1}{z - y}\]

Reproduce

herbie shell --seed 2020053 
(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)))