Average Error: 0.0 → 0.0
Time: 1.8s
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 r33288 = x;
        double r33289 = y;
        double r33290 = r33288 + r33289;
        double r33291 = 1.0;
        double r33292 = z;
        double r33293 = r33291 - r33292;
        double r33294 = r33290 * r33293;
        return r33294;
}
↓
double f(double x, double y, double z) {
        double r33295 = 1.0;
        double r33296 = x;
        double r33297 = y;
        double r33298 = r33295 * r33297;
        double r33299 = fma(r33295, r33296, r33298);
        double r33300 = z;
        double r33301 = -r33300;
        double r33302 = r33296 + r33297;
        double r33303 = r33301 * r33302;
        double r33304 = r33299 + r33303;
        return r33304;
}

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 2020060 +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)))