Average Error: 0.0 → 0.0
Time: 1.0s
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 r76929 = x;
        double r76930 = y;
        double r76931 = r76929 * r76930;
        double r76932 = z;
        double r76933 = t;
        double r76934 = r76932 * r76933;
        double r76935 = r76931 - r76934;
        return r76935;
}
↓
double f(double x, double y, double z, double t) {
        double r76936 = x;
        double r76937 = y;
        double r76938 = z;
        double r76939 = t;
        double r76940 = r76938 * r76939;
        double r76941 = -r76940;
        double r76942 = fma(r76936, r76937, r76941);
        return r76942;
}

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 2020047 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))