Average Error: 0.0 → 0.0
Time: 16.0s
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 r3122174 = x;
        double r3122175 = y;
        double r3122176 = r3122174 * r3122175;
        double r3122177 = z;
        double r3122178 = t;
        double r3122179 = r3122177 * r3122178;
        double r3122180 = r3122176 + r3122179;
        double r3122181 = a;
        double r3122182 = b;
        double r3122183 = r3122181 * r3122182;
        double r3122184 = r3122180 + r3122183;
        double r3122185 = c;
        double r3122186 = i;
        double r3122187 = r3122185 * r3122186;
        double r3122188 = r3122184 + r3122187;
        return r3122188;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3122189 = z;
        double r3122190 = t;
        double r3122191 = x;
        double r3122192 = y;
        double r3122193 = c;
        double r3122194 = i;
        double r3122195 = b;
        double r3122196 = a;
        double r3122197 = r3122195 * r3122196;
        double r3122198 = fma(r3122193, r3122194, r3122197);
        double r3122199 = fma(r3122191, r3122192, r3122198);
        double r3122200 = fma(r3122189, r3122190, r3122199);
        return r3122200;
}

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 2019162 +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)))