Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[1 \cdot \left(y - x \cdot y\right) + x \cdot z\]
\left(1 - x\right) \cdot y + x \cdot z
↓
1 \cdot \left(y - x \cdot y\right) + x \cdot z
double code(double x, double y, double z) {
	return (((1.0 - x) * y) + (x * z));
}
↓
double code(double x, double y, double z) {
	return ((1.0 * (y - (x * 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

Original0.0
Target0.0
Herbie0.0
\[y - x \cdot \left(y - z\right)\]

Derivation

  1. Initial program 0.0

    \[\left(1 - x\right) \cdot y + x \cdot z\]
  2. Using strategy rm

  3. Applied flip--8.2

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

  4. Applied associate-*l/10.4

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

  5. Taylor expanded around 0 0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (- y (* x (- y z)))

  (+ (* (- 1 x) y) (* x z)))