Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[z + x \cdot \left(y - z\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
z + x \cdot \left(y - z\right)
(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))
↓
(FPCore (x y z) :precision binary64 (+ z (* x (- y 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 z + (x * (y - 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

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020224 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))