Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\left(x + y\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, z, z \cdot y\right)\]
\left(x + y\right) \cdot z
↓
\mathsf{fma}\left(x, z, z \cdot y\right)
double code(double x, double y, double z) {
	return ((x + y) * z);
}
↓
double code(double x, double y, double z) {
	return fma(x, z, (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

    \[\left(x + y\right) \cdot z\]
  2. Using strategy rm

  3. Applied pow10.0

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

  4. Applied pow10.0

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

  5. Applied pow-prod-down0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))