Average Error: 10.1 → 0.0
Time: 6.7s
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)
(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 (x + (y * (z - x))) / z;
}
↓
double code(double x, double y, double z) {
	return y + ((x / z) - (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

Original10.1
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.1

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

  2. Taylor expanded around 0 3.4

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

  3. Simplified0.0

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

  5. Applied sub-neg_binary64_188260.0

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

  6. Applied distribute-rgt-in_binary64_187830.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(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))