Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[\left(x + y\right) \cdot \left(1 - z\right)\]
↓
\[\mathsf{fma}\left(x, -z, \mathsf{fma}\left(1, x, 1 \cdot y\right)\right) + y \cdot \left(-z\right)\]
\left(x + y\right) \cdot \left(1 - z\right)
↓
\mathsf{fma}\left(x, -z, \mathsf{fma}\left(1, x, 1 \cdot y\right)\right) + y \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r34736 = x;
        double r34737 = y;
        double r34738 = r34736 + r34737;
        double r34739 = 1.0;
        double r34740 = z;
        double r34741 = r34739 - r34740;
        double r34742 = r34738 * r34741;
        return r34742;
}
↓
double f(double x, double y, double z) {
        double r34743 = x;
        double r34744 = z;
        double r34745 = -r34744;
        double r34746 = 1.0;
        double r34747 = y;
        double r34748 = r34746 * r34747;
        double r34749 = fma(r34746, r34743, r34748);
        double r34750 = fma(r34743, r34745, r34749);
        double r34751 = r34747 * r34745;
        double r34752 = r34750 + r34751;
        return r34752;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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 distribute-rgt-in0.0

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

  9. Applied associate-+r+0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019352 +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)))