Average Error: 0.0 → 0.0
Time: 7.7s
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 r75614 = x;
        double r75615 = y;
        double r75616 = r75614 * r75615;
        double r75617 = z;
        double r75618 = t;
        double r75619 = r75617 * r75618;
        double r75620 = r75616 + r75619;
        double r75621 = a;
        double r75622 = b;
        double r75623 = r75621 * r75622;
        double r75624 = r75620 + r75623;
        double r75625 = c;
        double r75626 = i;
        double r75627 = r75625 * r75626;
        double r75628 = r75624 + r75627;
        return r75628;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r75629 = c;
        double r75630 = i;
        double r75631 = a;
        double r75632 = b;
        double r75633 = x;
        double r75634 = y;
        double r75635 = z;
        double r75636 = t;
        double r75637 = r75635 * r75636;
        double r75638 = fma(r75633, r75634, r75637);
        double r75639 = fma(r75631, r75632, r75638);
        double r75640 = fma(r75629, r75630, r75639);
        return r75640;
}

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 2019323 +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)))