Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[1 \cdot x + \mathsf{fma}\left(x, z, \mathsf{fma}\left(z, y, 1 \cdot y\right)\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
1 \cdot x + \mathsf{fma}\left(x, z, \mathsf{fma}\left(z, y, 1 \cdot y\right)\right)
double code(double x, double y, double z) {
	return ((x + y) * (z + 1.0));
}
↓
double code(double x, double y, double z) {
	return ((1.0 * x) + fma(x, z, fma(z, y, (1.0 * 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 +-commutative0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

    \[\leadsto \mathsf{fma}\left(1, x, 1 \cdot y\right) + \color{blue}{z \cdot \left(x + y\right)}\]
  7. Using strategy rm

  8. Applied fma-udef0.0

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

  9. Applied associate-+l+0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

    \[\leadsto 1 \cdot x + \mathsf{fma}\left(x, z, \mathsf{fma}\left(z, y, 1 \cdot y\right)\right)\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1)))