Average Error: 0.0 → 0.0
Time: 9.7s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\]
\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 r68181 = x;
        double r68182 = y;
        double r68183 = r68181 * r68182;
        double r68184 = z;
        double r68185 = t;
        double r68186 = r68184 * r68185;
        double r68187 = r68183 + r68186;
        double r68188 = a;
        double r68189 = b;
        double r68190 = r68188 * r68189;
        double r68191 = r68187 + r68190;
        double r68192 = c;
        double r68193 = i;
        double r68194 = r68192 * r68193;
        double r68195 = r68191 + r68194;
        return r68195;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68196 = c;
        double r68197 = i;
        double r68198 = a;
        double r68199 = b;
        double r68200 = x;
        double r68201 = y;
        double r68202 = z;
        double r68203 = t;
        double r68204 = r68202 * r68203;
        double r68205 = fma(r68200, r68201, r68204);
        double r68206 = fma(r68198, r68199, r68205);
        double r68207 = fma(r68196, r68197, r68206);
        return r68207;
}

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 2019198 +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)))