Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[x \cdot y + \left(1 - x\right) \cdot z \]
↓
\[\mathsf{fma}\left(x, y - z, z\right) \]
x \cdot y + \left(1 - x\right) \cdot z
↓
\mathsf{fma}\left(x, y - z, z\right)

(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))
↓
(FPCore (x y z) :precision binary64 (fma x (- y z) z))
double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}
↓
double code(double x, double y, double z) {
	return fma(x, (y - z), z);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y - z, z\right)} \]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y - z, z\right) \]

Reproduce

herbie shell --seed 2021329 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))