Average Error: 0.0 → 0.0
Time: 758.0ms
Precision: 64
\[\left(x + y\right) \cdot \left(1 - z\right)\]
↓
\[\mathsf{fma}\left(1, x, 1 \cdot y\right) + \left(-z\right) \cdot \left(x + y\right)\]
\left(x + y\right) \cdot \left(1 - z\right)
↓
\mathsf{fma}\left(1, x, 1 \cdot y\right) + \left(-z\right) \cdot \left(x + y\right)
double f(double x, double y, double z) {
        double r44975 = x;
        double r44976 = y;
        double r44977 = r44975 + r44976;
        double r44978 = 1.0;
        double r44979 = z;
        double r44980 = r44978 - r44979;
        double r44981 = r44977 * r44980;
        return r44981;
}
↓
double f(double x, double y, double z) {
        double r44982 = 1.0;
        double r44983 = x;
        double r44984 = y;
        double r44985 = r44982 * r44984;
        double r44986 = fma(r44982, r44983, r44985);
        double r44987 = z;
        double r44988 = -r44987;
        double r44989 = r44983 + r44984;
        double r44990 = r44988 * r44989;
        double r44991 = r44986 + r44990;
        return r44991;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +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)))