Average Error: 0.0 → 0.0
Time: 6.5s
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 r115410 = x;
        double r115411 = y;
        double r115412 = r115410 * r115411;
        double r115413 = z;
        double r115414 = t;
        double r115415 = r115413 * r115414;
        double r115416 = r115412 + r115415;
        double r115417 = a;
        double r115418 = b;
        double r115419 = r115417 * r115418;
        double r115420 = r115416 + r115419;
        double r115421 = c;
        double r115422 = i;
        double r115423 = r115421 * r115422;
        double r115424 = r115420 + r115423;
        return r115424;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r115425 = i;
        double r115426 = c;
        double r115427 = b;
        double r115428 = a;
        double r115429 = x;
        double r115430 = y;
        double r115431 = z;
        double r115432 = t;
        double r115433 = r115431 * r115432;
        double r115434 = fma(r115429, r115430, r115433);
        double r115435 = fma(r115427, r115428, r115434);
        double r115436 = fma(r115425, r115426, r115435);
        return r115436;
}

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 2019353 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))