Average Error: 0.0 → 0.0
Time: 2.7s
Precision: binary64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[y + \left(x \cdot z + \left(x + y \cdot z\right)\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
y + \left(x \cdot z + \left(x + y \cdot z\right)\right)
(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))
↓
(FPCore (x y z) :precision binary64 (+ y (+ (* x z) (+ x (* y z)))))
double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}
↓
double code(double x, double y, double z) {
	return y + ((x * 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

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

  2. Taylor expanded around 0 0.0

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

  3. Final simplification0.0

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

Alternatives

Reproduce

herbie shell --seed 2021118 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))