Average Error: 0.0 → 0.0
Time: 21.2s
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 r58815 = x;
        double r58816 = y;
        double r58817 = r58815 * r58816;
        double r58818 = z;
        double r58819 = t;
        double r58820 = r58818 * r58819;
        double r58821 = r58817 + r58820;
        double r58822 = a;
        double r58823 = b;
        double r58824 = r58822 * r58823;
        double r58825 = r58821 + r58824;
        double r58826 = c;
        double r58827 = i;
        double r58828 = r58826 * r58827;
        double r58829 = r58825 + r58828;
        return r58829;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r58830 = c;
        double r58831 = i;
        double r58832 = a;
        double r58833 = b;
        double r58834 = x;
        double r58835 = y;
        double r58836 = z;
        double r58837 = t;
        double r58838 = r58836 * r58837;
        double r58839 = fma(r58834, r58835, r58838);
        double r58840 = fma(r58832, r58833, r58839);
        double r58841 = fma(r58830, r58831, r58840);
        return r58841;
}

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 2019325 +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)))