Average Error: 0.0 → 0.0
Time: 1.4s
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 r40216 = x;
        double r40217 = y;
        double r40218 = r40216 + r40217;
        double r40219 = 1.0;
        double r40220 = z;
        double r40221 = r40219 - r40220;
        double r40222 = r40218 * r40221;
        return r40222;
}
↓
double f(double x, double y, double z) {
        double r40223 = 1.0;
        double r40224 = x;
        double r40225 = y;
        double r40226 = r40223 * r40225;
        double r40227 = fma(r40223, r40224, r40226);
        double r40228 = z;
        double r40229 = -r40228;
        double r40230 = r40224 + r40225;
        double r40231 = r40229 * r40230;
        double r40232 = r40227 + r40231;
        return r40232;
}

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 2019347 +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)))