Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r125254 = x;
        double r125255 = y;
        double r125256 = r125254 * r125255;
        double r125257 = z;
        double r125258 = t;
        double r125259 = r125257 * r125258;
        double r125260 = r125256 + r125259;
        double r125261 = a;
        double r125262 = b;
        double r125263 = r125261 * r125262;
        double r125264 = r125260 + r125263;
        double r125265 = c;
        double r125266 = i;
        double r125267 = r125265 * r125266;
        double r125268 = r125264 + r125267;
        return r125268;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r125269 = i;
        double r125270 = c;
        double r125271 = b;
        double r125272 = a;
        double r125273 = x;
        double r125274 = y;
        double r125275 = z;
        double r125276 = t;
        double r125277 = r125275 * r125276;
        double r125278 = fma(r125273, r125274, r125277);
        double r125279 = fma(r125271, r125272, r125278);
        double r125280 = fma(r125269, r125270, r125279);
        return r125280;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Derivation

  1. Initial program 0.0

    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\]

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))