Average Error: 10.4 → 0.0
Time: 11.5min
Precision: binary64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(1 - y\right) \cdot \frac{x}{z} + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(1 - y\right) \cdot \frac{x}{z} + y
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) (((double) (1.0 - y)) * (x / z))) + 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

Original10.4
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.4

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

  2. Taylor expanded around 0 3.4

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

  3. Simplified3.4

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

  5. Applied *-un-lft-identity3.4

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

  6. Applied times-frac0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

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))