Average Error: 0.0 → 0.0
Time: 6.6s
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 r5887194 = x;
        double r5887195 = y;
        double r5887196 = r5887194 * r5887195;
        double r5887197 = z;
        double r5887198 = t;
        double r5887199 = r5887197 * r5887198;
        double r5887200 = r5887196 - r5887199;
        return r5887200;
}
↓
double f(double x, double y, double z, double t) {
        double r5887201 = x;
        double r5887202 = y;
        double r5887203 = z;
        double r5887204 = t;
        double r5887205 = r5887203 * r5887204;
        double r5887206 = -r5887205;
        double r5887207 = fma(r5887201, r5887202, r5887206);
        return r5887207;
}

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 2019163 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))