Average Error: 0.0 → 0.0
Time: 11.5s
Precision: binary64
\[\left(x \cdot y + z \cdot t\right) + a \cdot b\]
↓
\[a \cdot b + \left(x \cdot y + z \cdot t\right)\]
\left(x \cdot y + z \cdot t\right) + a \cdot b
↓
a \cdot b + \left(x \cdot y + z \cdot t\right)
(FPCore (x y z t a b) :precision binary64 (+ (+ (* x y) (* z t)) (* a b)))
↓
(FPCore (x y z t a b) :precision binary64 (+ (* a b) (+ (* x y) (* z t))))
double code(double x, double y, double z, double t, double a, double b) {
	return ((x * y) + (z * t)) + (a * b);
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return (a * b) + ((x * y) + (z * t));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x \cdot y + z \cdot t\right) + a \cdot b\]
  2. Using strategy rm

  3. Applied +-commutative_binary64_51230.0

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

  4. Final simplification0.0

    \[\leadsto a \cdot b + \left(x \cdot y + z \cdot t\right)\]

Reproduce

herbie shell --seed 2021076 
(FPCore (x y z t a b)
  :name "Linear.V3:$cdot from linear-1.19.1.3, B"
  :precision binary64
  (+ (+ (* x y) (* z t)) (* a b)))