Average Error: 0.0 → 0.0
Time: 16.9s
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 r2618425 = x;
        double r2618426 = y;
        double r2618427 = r2618425 * r2618426;
        double r2618428 = z;
        double r2618429 = t;
        double r2618430 = r2618428 * r2618429;
        double r2618431 = r2618427 + r2618430;
        double r2618432 = a;
        double r2618433 = b;
        double r2618434 = r2618432 * r2618433;
        double r2618435 = r2618431 + r2618434;
        double r2618436 = c;
        double r2618437 = i;
        double r2618438 = r2618436 * r2618437;
        double r2618439 = r2618435 + r2618438;
        return r2618439;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2618440 = z;
        double r2618441 = t;
        double r2618442 = x;
        double r2618443 = y;
        double r2618444 = c;
        double r2618445 = i;
        double r2618446 = b;
        double r2618447 = a;
        double r2618448 = r2618446 * r2618447;
        double r2618449 = fma(r2618444, r2618445, r2618448);
        double r2618450 = fma(r2618442, r2618443, r2618449);
        double r2618451 = fma(r2618440, r2618441, r2618450);
        return r2618451;
}

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 2019162 +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)))