Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[\left(x + y\right) \cdot \left(1 - z\right)\]
↓
\[\mathsf{fma}\left(y, -z, \mathsf{fma}\left(1, x, 1 \cdot y\right)\right) + \left(-z\right) \cdot x\]
\left(x + y\right) \cdot \left(1 - z\right)
↓
\mathsf{fma}\left(y, -z, \mathsf{fma}\left(1, x, 1 \cdot y\right)\right) + \left(-z\right) \cdot x
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) fma(y, ((double) -(z)), ((double) fma(1.0, x, ((double) (1.0 * y)))))) + ((double) (((double) -(z)) * x))));
}

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 +-commutative0.0

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

  9. Applied distribute-lft-in0.0

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

  10. Applied associate-+r+0.0

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

  11. Simplified0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2020114 +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)))