Average Error: 0.0 → 0.0
Time: 4.7s
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 r4397505 = x;
        double r4397506 = y;
        double r4397507 = r4397505 * r4397506;
        double r4397508 = z;
        double r4397509 = t;
        double r4397510 = r4397508 * r4397509;
        double r4397511 = r4397507 - r4397510;
        return r4397511;
}
↓
double f(double x, double y, double z, double t) {
        double r4397512 = x;
        double r4397513 = y;
        double r4397514 = z;
        double r4397515 = t;
        double r4397516 = r4397514 * r4397515;
        double r4397517 = -r4397516;
        double r4397518 = fma(r4397512, r4397513, r4397517);
        return r4397518;
}

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 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))