Average Error: 0.0 → 0.0
Time: 9.7s
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 r6037160 = x;
        double r6037161 = y;
        double r6037162 = r6037160 * r6037161;
        double r6037163 = z;
        double r6037164 = t;
        double r6037165 = r6037163 * r6037164;
        double r6037166 = r6037162 + r6037165;
        double r6037167 = a;
        double r6037168 = b;
        double r6037169 = r6037167 * r6037168;
        double r6037170 = r6037166 + r6037169;
        double r6037171 = c;
        double r6037172 = i;
        double r6037173 = r6037171 * r6037172;
        double r6037174 = r6037170 + r6037173;
        return r6037174;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6037175 = z;
        double r6037176 = t;
        double r6037177 = x;
        double r6037178 = y;
        double r6037179 = c;
        double r6037180 = i;
        double r6037181 = b;
        double r6037182 = a;
        double r6037183 = r6037181 * r6037182;
        double r6037184 = fma(r6037179, r6037180, r6037183);
        double r6037185 = fma(r6037177, r6037178, r6037184);
        double r6037186 = fma(r6037175, r6037176, r6037185);
        return r6037186;
}

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 2019164 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))