Average Error: 0.0 → 0.0
Time: 2.8s
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 r39666 = x;
        double r39667 = y;
        double r39668 = r39666 + r39667;
        double r39669 = 1.0;
        double r39670 = z;
        double r39671 = r39669 - r39670;
        double r39672 = r39668 * r39671;
        return r39672;
}
↓
double f(double x, double y, double z) {
        double r39673 = 1.0;
        double r39674 = x;
        double r39675 = y;
        double r39676 = r39673 * r39675;
        double r39677 = fma(r39673, r39674, r39676);
        double r39678 = z;
        double r39679 = -r39678;
        double r39680 = r39674 + r39675;
        double r39681 = r39679 * r39680;
        double r39682 = r39677 + r39681;
        return r39682;
}

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 2020062 +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)))