Average Error: 0.0 → 0.0
Time: 17.3s
Precision: binary64
Cost: 576
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[x \cdot y + z \cdot \left(1 - x\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
x \cdot y + z \cdot \left(1 - x\right)
(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))
↓
(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 x))))
double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}
↓
double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - x));
}

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. Using strategy rm

  3. Applied *-un-lft-identity_binary64_58750.0

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

  4. Applied associate-*l*_binary64_58160.0

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

  6. Applied *-un-lft-identity_binary64_58750.0

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

  8. Applied *-commutative_binary64_58060.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020322 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))