Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[z \cdot \left(x + y\right) + \mathsf{fma}\left(1, x, 1 \cdot y\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
z \cdot \left(x + y\right) + \mathsf{fma}\left(1, x, 1 \cdot y\right)
double f(double x, double y, double z) {
        double r16803 = x;
        double r16804 = y;
        double r16805 = r16803 + r16804;
        double r16806 = z;
        double r16807 = 1.0;
        double r16808 = r16806 + r16807;
        double r16809 = r16805 * r16808;
        return r16809;
}
↓
double f(double x, double y, double z) {
        double r16810 = z;
        double r16811 = x;
        double r16812 = y;
        double r16813 = r16811 + r16812;
        double r16814 = r16810 * r16813;
        double r16815 = 1.0;
        double r16816 = r16815 * r16812;
        double r16817 = fma(r16815, r16811, r16816);
        double r16818 = r16814 + r16817;
        return r16818;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) \cdot \left(z + 1\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(x + y\right) \cdot z + \left(x + y\right) \cdot 1}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{z \cdot \left(x + y\right)} + \left(x + y\right) \cdot 1\]

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1)))