Average Error: 0.0 → 0.0
Time: 8.3s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \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 r59406 = x;
        double r59407 = y;
        double r59408 = r59406 * r59407;
        double r59409 = z;
        double r59410 = t;
        double r59411 = r59409 * r59410;
        double r59412 = r59408 + r59411;
        double r59413 = a;
        double r59414 = b;
        double r59415 = r59413 * r59414;
        double r59416 = r59412 + r59415;
        double r59417 = c;
        double r59418 = i;
        double r59419 = r59417 * r59418;
        double r59420 = r59416 + r59419;
        return r59420;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59421 = c;
        double r59422 = i;
        double r59423 = a;
        double r59424 = b;
        double r59425 = x;
        double r59426 = y;
        double r59427 = z;
        double r59428 = t;
        double r59429 = r59427 * r59428;
        double r59430 = fma(r59425, r59426, r59429);
        double r59431 = fma(r59423, r59424, r59430);
        double r59432 = fma(r59421, r59422, r59431);
        return r59432;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))