Average Error: 0.0 → 0.0
Time: 5.9s
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 r2525436 = x;
        double r2525437 = y;
        double r2525438 = r2525436 * r2525437;
        double r2525439 = z;
        double r2525440 = t;
        double r2525441 = r2525439 * r2525440;
        double r2525442 = r2525438 + r2525441;
        double r2525443 = a;
        double r2525444 = b;
        double r2525445 = r2525443 * r2525444;
        double r2525446 = r2525442 + r2525445;
        double r2525447 = c;
        double r2525448 = i;
        double r2525449 = r2525447 * r2525448;
        double r2525450 = r2525446 + r2525449;
        return r2525450;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2525451 = z;
        double r2525452 = t;
        double r2525453 = x;
        double r2525454 = y;
        double r2525455 = c;
        double r2525456 = i;
        double r2525457 = b;
        double r2525458 = a;
        double r2525459 = r2525457 * r2525458;
        double r2525460 = fma(r2525455, r2525456, r2525459);
        double r2525461 = fma(r2525453, r2525454, r2525460);
        double r2525462 = fma(r2525451, r2525452, r2525461);
        return r2525462;
}

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 2019168 +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)))