Average Error: 10.2 → 0.0
Time: 2.8s
Precision: binary64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(y + \frac{x}{z}\right) - y \cdot \frac{x}{z}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(y + \frac{x}{z}\right) - y \cdot \frac{x}{z}
(FPCore (x y z) :precision binary64 (/ (+ x (* y (- z x))) z))
↓
(FPCore (x y z) :precision binary64 (- (+ y (/ x z)) (* y (/ x z))))
double code(double x, double y, double z) {
	return (((double) (x + ((double) (y * ((double) (z - x)))))) / z);
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (y + (x / z))) - ((double) (y * (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

Original10.2
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.2

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

  3. Applied add-cube-cbrt_binary6410.8

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

  4. Applied associate-*r*_binary6410.8

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

  5. Taylor expanded around 0 3.6

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020205 
(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))