Average Error: 0.0 → 0.0
Time: 33.6s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(z, t, x \cdot y\right)\right)\right)\]
\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(z, t, x \cdot y\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4069985 = x;
        double r4069986 = y;
        double r4069987 = r4069985 * r4069986;
        double r4069988 = z;
        double r4069989 = t;
        double r4069990 = r4069988 * r4069989;
        double r4069991 = r4069987 + r4069990;
        double r4069992 = a;
        double r4069993 = b;
        double r4069994 = r4069992 * r4069993;
        double r4069995 = r4069991 + r4069994;
        double r4069996 = c;
        double r4069997 = i;
        double r4069998 = r4069996 * r4069997;
        double r4069999 = r4069995 + r4069998;
        return r4069999;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4070000 = c;
        double r4070001 = i;
        double r4070002 = a;
        double r4070003 = b;
        double r4070004 = z;
        double r4070005 = t;
        double r4070006 = x;
        double r4070007 = y;
        double r4070008 = r4070006 * r4070007;
        double r4070009 = fma(r4070004, r4070005, r4070008);
        double r4070010 = fma(r4070002, r4070003, r4070009);
        double r4070011 = fma(r4070000, r4070001, r4070010);
        return r4070011;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(z, t, y \cdot x\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(z, t, x \cdot y\right)\right)\right)\]

Reproduce

herbie shell --seed 2019200 +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)))