Average Error: 0.0 → 0.0
Time: 2.4s
Precision: binary64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[x + \left(x \cdot z + \left(y + z \cdot y\right)\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
x + \left(x \cdot z + \left(y + z \cdot y\right)\right)
(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))
↓
(FPCore (x y z) :precision binary64 (+ x (+ (* x z) (+ y (* z y)))))
double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}
↓
double code(double x, double y, double z) {
	return x + ((x * z) + (y + (z * y)));
}

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. Using strategy rm

  3. Applied flip-+_binary648.1

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

  4. Applied associate-*r/_binary6412.1

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

  5. Simplified12.1

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

  6. Taylor expanded around inf 0.0

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

  7. Final simplification0.0

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

Alternatives

Reproduce

herbie shell --seed 2021110 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))