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 r92008 = x;
        double r92009 = y;
        double r92010 = r92008 * r92009;
        double r92011 = z;
        double r92012 = t;
        double r92013 = r92011 * r92012;
        double r92014 = r92010 - r92013;
        return r92014;
}
↓
double f(double x, double y, double z, double t) {
        double r92015 = x;
        double r92016 = y;
        double r92017 = z;
        double r92018 = t;
        double r92019 = r92017 * r92018;
        double r92020 = -r92019;
        double r92021 = fma(r92015, r92016, r92020);
        return r92021;
}

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)))