Average Error: 0.0 → 0.0
Time: 5.0s
Precision: binary64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[\left(x \cdot z + z \cdot y\right) + \left(x + y\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
\left(x \cdot z + z \cdot y\right) + \left(x + y\right)
(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))
↓
(FPCore (x y z) :precision binary64 (+ (+ (* x z) (* z y)) (+ x 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 * z) + (z * y)) + (x + 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 distribute-rgt-in_binary64_10510.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Taylor expanded around 0 0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2021098 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))