Average Error: 0.0 → 0.0
Time: 10.5s
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 r3131758 = x;
        double r3131759 = y;
        double r3131760 = r3131758 * r3131759;
        double r3131761 = z;
        double r3131762 = t;
        double r3131763 = r3131761 * r3131762;
        double r3131764 = r3131760 + r3131763;
        double r3131765 = a;
        double r3131766 = b;
        double r3131767 = r3131765 * r3131766;
        double r3131768 = r3131764 + r3131767;
        double r3131769 = c;
        double r3131770 = i;
        double r3131771 = r3131769 * r3131770;
        double r3131772 = r3131768 + r3131771;
        return r3131772;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3131773 = z;
        double r3131774 = t;
        double r3131775 = x;
        double r3131776 = y;
        double r3131777 = c;
        double r3131778 = i;
        double r3131779 = b;
        double r3131780 = a;
        double r3131781 = r3131779 * r3131780;
        double r3131782 = fma(r3131777, r3131778, r3131781);
        double r3131783 = fma(r3131775, r3131776, r3131782);
        double r3131784 = fma(r3131773, r3131774, r3131783);
        return r3131784;
}

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 2019158 +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)))