Average Error: 0.0 → 0.0
Time: 9.1s
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 r81185 = x;
        double r81186 = y;
        double r81187 = r81185 * r81186;
        double r81188 = z;
        double r81189 = t;
        double r81190 = r81188 * r81189;
        double r81191 = r81187 + r81190;
        double r81192 = a;
        double r81193 = b;
        double r81194 = r81192 * r81193;
        double r81195 = r81191 + r81194;
        double r81196 = c;
        double r81197 = i;
        double r81198 = r81196 * r81197;
        double r81199 = r81195 + r81198;
        return r81199;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r81200 = c;
        double r81201 = i;
        double r81202 = a;
        double r81203 = b;
        double r81204 = x;
        double r81205 = y;
        double r81206 = z;
        double r81207 = t;
        double r81208 = r81206 * r81207;
        double r81209 = fma(r81204, r81205, r81208);
        double r81210 = fma(r81202, r81203, r81209);
        double r81211 = fma(r81200, r81201, r81210);
        return r81211;
}

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 2019351 +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)))