Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1041503 = x;
        double r1041504 = y;
        double r1041505 = r1041503 * r1041504;
        double r1041506 = z;
        double r1041507 = t;
        double r1041508 = r1041506 * r1041507;
        double r1041509 = r1041505 + r1041508;
        double r1041510 = a;
        double r1041511 = b;
        double r1041512 = r1041510 * r1041511;
        double r1041513 = r1041509 + r1041512;
        double r1041514 = c;
        double r1041515 = i;
        double r1041516 = r1041514 * r1041515;
        double r1041517 = r1041513 + r1041516;
        return r1041517;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1041518 = z;
        double r1041519 = t;
        double r1041520 = x;
        double r1041521 = y;
        double r1041522 = c;
        double r1041523 = i;
        double r1041524 = b;
        double r1041525 = a;
        double r1041526 = r1041524 * r1041525;
        double r1041527 = fma(r1041522, r1041523, r1041526);
        double r1041528 = fma(r1041520, r1041521, r1041527);
        double r1041529 = fma(r1041518, r1041519, r1041528);
        return r1041529;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 +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)))