Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[\left(x + y\right) \cdot \left(1 - z\right)\]
↓
\[1 \cdot x + \mathsf{fma}\left(1, y, \left(-z\right) \cdot \left(x + y\right)\right)\]
\left(x + y\right) \cdot \left(1 - z\right)
↓
1 \cdot x + \mathsf{fma}\left(1, y, \left(-z\right) \cdot \left(x + y\right)\right)
double code(double x, double y, double z) {
	return ((double) (((double) (x + y)) * ((double) (1.0 - z))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (1.0 * x)) + ((double) fma(1.0, y, ((double) (((double) -(z)) * ((double) (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

    \[\left(x + y\right) \cdot \left(1 - z\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  8. Applied fma-udef0.0

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

  9. Applied associate-+l+0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2020120 +o rules:numerics
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1 z)))