Average Error: 0.0 → 0.0
Time: 20.7s
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 r68142 = x;
        double r68143 = y;
        double r68144 = r68142 * r68143;
        double r68145 = z;
        double r68146 = t;
        double r68147 = r68145 * r68146;
        double r68148 = r68144 + r68147;
        double r68149 = a;
        double r68150 = b;
        double r68151 = r68149 * r68150;
        double r68152 = r68148 + r68151;
        double r68153 = c;
        double r68154 = i;
        double r68155 = r68153 * r68154;
        double r68156 = r68152 + r68155;
        return r68156;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68157 = c;
        double r68158 = i;
        double r68159 = a;
        double r68160 = b;
        double r68161 = x;
        double r68162 = y;
        double r68163 = z;
        double r68164 = t;
        double r68165 = r68163 * r68164;
        double r68166 = fma(r68161, r68162, r68165);
        double r68167 = fma(r68159, r68160, r68166);
        double r68168 = fma(r68157, r68158, r68167);
        return r68168;
}

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)))