Average Error: 0.0 → 0.0
Time: 4.0s
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 r1162771 = x;
        double r1162772 = y;
        double r1162773 = r1162771 * r1162772;
        double r1162774 = z;
        double r1162775 = t;
        double r1162776 = r1162774 * r1162775;
        double r1162777 = r1162773 + r1162776;
        double r1162778 = a;
        double r1162779 = b;
        double r1162780 = r1162778 * r1162779;
        double r1162781 = r1162777 + r1162780;
        double r1162782 = c;
        double r1162783 = i;
        double r1162784 = r1162782 * r1162783;
        double r1162785 = r1162781 + r1162784;
        return r1162785;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1162786 = z;
        double r1162787 = t;
        double r1162788 = x;
        double r1162789 = y;
        double r1162790 = c;
        double r1162791 = i;
        double r1162792 = b;
        double r1162793 = a;
        double r1162794 = r1162792 * r1162793;
        double r1162795 = fma(r1162790, r1162791, r1162794);
        double r1162796 = fma(r1162788, r1162789, r1162795);
        double r1162797 = fma(r1162786, r1162787, r1162796);
        return r1162797;
}

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)))