Average Error: 9.8 → 0.1
Time: 2.7s
Precision: binary64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \frac{x}{z} \cdot \left(1 - y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \frac{x}{z} \cdot \left(1 - y\right)
double code(double x, double y, double z) {
	return ((double) (((double) (x + ((double) (y * ((double) (z - x)))))) / z));
}
↓
double code(double x, double y, double z) {
	return ((double) (y + ((double) (((double) (x / z)) * ((double) (1.0 - y))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.8
Target0.0
Herbie0.1
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.8

    \[\frac{x + y \cdot \left(z - x\right)}{z}\]

  2. Simplified4.0

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

  4. Applied associate-*r/3.4

    \[\leadsto y + \color{blue}{\frac{x \cdot \left(1 - y\right)}{z}}\]

  5. Simplified3.4

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

  7. Applied clear-num3.5

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

  8. Taylor expanded around 0 3.4

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

  9. Simplified0.1

    \[\leadsto y + \color{blue}{\frac{x}{z} \cdot \left(1 - y\right)}\]

  10. Final simplification0.1

    \[\leadsto y + \frac{x}{z} \cdot \left(1 - y\right)\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

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

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