Average Error: 0.0 → 0.0
Time: 6.5s
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 r4900221 = x;
        double r4900222 = y;
        double r4900223 = r4900221 * r4900222;
        double r4900224 = z;
        double r4900225 = t;
        double r4900226 = r4900224 * r4900225;
        double r4900227 = r4900223 - r4900226;
        return r4900227;
}
↓
double f(double x, double y, double z, double t) {
        double r4900228 = x;
        double r4900229 = y;
        double r4900230 = z;
        double r4900231 = t;
        double r4900232 = r4900230 * r4900231;
        double r4900233 = -r4900232;
        double r4900234 = fma(r4900228, r4900229, r4900233);
        return r4900234;
}

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 2019164 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))