Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[\mathsf{fma}\left(x, z, \mathsf{fma}\left(1, x, 1 \cdot y\right)\right) + z \cdot y\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
\mathsf{fma}\left(x, z, \mathsf{fma}\left(1, x, 1 \cdot y\right)\right) + z \cdot y
double code(double x, double y, double z) {
	return ((double) (((double) (x + y)) * ((double) (z + 1.0))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) fma(x, z, ((double) fma(1.0, x, ((double) (1.0 * y)))))) + ((double) (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 +-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 distribute-lft-in0.0

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

  9. Applied associate-+r+0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2020113 +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)))