Average Error: 9.9 → 0.0
Time: 2.8s
Precision: binary64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \left(\frac{x}{z} - y \cdot \frac{x}{z}\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \left(\frac{x}{z} - y \cdot \frac{x}{z}\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 * ((double) (x / z))))))));
}

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

Original9.9
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.9

    \[\frac{x + y \cdot \left(z - x\right)}{z}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt10.5

    \[\leadsto \frac{x + \color{blue}{\left(\sqrt[3]{y \cdot \left(z - x\right)} \cdot \sqrt[3]{y \cdot \left(z - x\right)}\right) \cdot \sqrt[3]{y \cdot \left(z - x\right)}}}{z}\]

  4. Taylor expanded around 0 3.4

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020185 
(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))