Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[x \cdot y + z \cdot t\]
↓
\[\mathsf{fma}\left(x, y, z \cdot t\right)\]
x \cdot y + z \cdot t
↓
\mathsf{fma}\left(x, y, z \cdot t\right)
double f(double x, double y, double z, double t) {
        double r160615 = x;
        double r160616 = y;
        double r160617 = r160615 * r160616;
        double r160618 = z;
        double r160619 = t;
        double r160620 = r160618 * r160619;
        double r160621 = r160617 + r160620;
        return r160621;
}
↓
double f(double x, double y, double z, double t) {
        double r160622 = x;
        double r160623 = y;
        double r160624 = z;
        double r160625 = t;
        double r160626 = r160624 * r160625;
        double r160627 = fma(r160622, r160623, r160626);
        return r160627;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot t\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))