Average Error: 0.0 → 0.0
Time: 47.7s
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 r6635638 = x;
        double r6635639 = y;
        double r6635640 = r6635638 * r6635639;
        double r6635641 = z;
        double r6635642 = t;
        double r6635643 = r6635641 * r6635642;
        double r6635644 = r6635640 - r6635643;
        return r6635644;
}
↓
double f(double x, double y, double z, double t) {
        double r6635645 = x;
        double r6635646 = y;
        double r6635647 = z;
        double r6635648 = t;
        double r6635649 = r6635647 * r6635648;
        double r6635650 = -r6635649;
        double r6635651 = fma(r6635645, r6635646, r6635650);
        return r6635651;
}

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. Using strategy rm

  3. Applied fma-neg0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))