Average Error: 9.4 → 0.0
Time: 2.7s
Precision: binary64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y - \frac{x}{z} \cdot \left(y - 1\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y - \frac{x}{z} \cdot \left(y - 1\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) (y - 1.0))))));
}

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

Original9.4
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.4

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

  2. Taylor expanded around 0 3.0

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

  3. Simplified3.0

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

  5. Applied div-sub3.0

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

  6. Simplified3.1

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

  7. Taylor expanded around 0 3.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020181 
(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))