Average Error: 0.0 → 0.0
Time: 1.7s
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 r33520 = x;
        double r33521 = y;
        double r33522 = r33520 + r33521;
        double r33523 = 1.0;
        double r33524 = z;
        double r33525 = r33523 - r33524;
        double r33526 = r33522 * r33525;
        return r33526;
}
↓
double f(double x, double y, double z) {
        double r33527 = 1.0;
        double r33528 = x;
        double r33529 = y;
        double r33530 = r33527 * r33529;
        double r33531 = fma(r33527, r33528, r33530);
        double r33532 = z;
        double r33533 = -r33532;
        double r33534 = r33528 + r33529;
        double r33535 = r33533 * r33534;
        double r33536 = r33531 + r33535;
        return r33536;
}

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)))