Average Error: 0.0 → 0.0
Time: 19.5s
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 r77168 = x;
        double r77169 = y;
        double r77170 = r77168 * r77169;
        double r77171 = z;
        double r77172 = t;
        double r77173 = r77171 * r77172;
        double r77174 = r77170 + r77173;
        double r77175 = a;
        double r77176 = b;
        double r77177 = r77175 * r77176;
        double r77178 = r77174 + r77177;
        double r77179 = c;
        double r77180 = i;
        double r77181 = r77179 * r77180;
        double r77182 = r77178 + r77181;
        return r77182;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77183 = c;
        double r77184 = i;
        double r77185 = a;
        double r77186 = b;
        double r77187 = x;
        double r77188 = y;
        double r77189 = z;
        double r77190 = t;
        double r77191 = r77189 * r77190;
        double r77192 = fma(r77187, r77188, r77191);
        double r77193 = fma(r77185, r77186, r77192);
        double r77194 = fma(r77183, r77184, r77193);
        return r77194;
}

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)))