Average Error: 0.0 → 0.0
Time: 1.8s
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 r104521 = x;
        double r104522 = y;
        double r104523 = r104521 * r104522;
        double r104524 = z;
        double r104525 = t;
        double r104526 = r104524 * r104525;
        double r104527 = r104523 - r104526;
        return r104527;
}
↓
double f(double x, double y, double z, double t) {
        double r104528 = x;
        double r104529 = y;
        double r104530 = z;
        double r104531 = t;
        double r104532 = r104530 * r104531;
        double r104533 = -r104532;
        double r104534 = fma(r104528, r104529, r104533);
        return r104534;
}

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 2020001 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))