Average Error: 0.0 → 0.0
Time: 5.8s
Precision: binary64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[y + \left(x + \left(y \cdot z + z \cdot x\right)\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
y + \left(x + \left(y \cdot z + z \cdot x\right)\right)
(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))
↓
(FPCore (x y z) :precision binary64 (+ y (+ x (+ (* y z) (* z x)))))
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 + ((y * z) + (z * 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

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  5. Applied distribute-lft-in_binary64_10500.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2021176 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))