Average Error: 0.0 → 0.0
Time: 2.0s
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 r126802 = x;
        double r126803 = y;
        double r126804 = r126802 * r126803;
        double r126805 = z;
        double r126806 = t;
        double r126807 = r126805 * r126806;
        double r126808 = r126804 - r126807;
        return r126808;
}
↓
double f(double x, double y, double z, double t) {
        double r126809 = x;
        double r126810 = y;
        double r126811 = z;
        double r126812 = t;
        double r126813 = r126811 * r126812;
        double r126814 = -r126813;
        double r126815 = fma(r126809, r126810, r126814);
        return r126815;
}

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 2020046 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))