Average Error: 0.0 → 0.0
Time: 20.7s
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 r3632263 = x;
        double r3632264 = y;
        double r3632265 = r3632263 * r3632264;
        double r3632266 = z;
        double r3632267 = t;
        double r3632268 = r3632266 * r3632267;
        double r3632269 = r3632265 + r3632268;
        double r3632270 = a;
        double r3632271 = b;
        double r3632272 = r3632270 * r3632271;
        double r3632273 = r3632269 + r3632272;
        double r3632274 = c;
        double r3632275 = i;
        double r3632276 = r3632274 * r3632275;
        double r3632277 = r3632273 + r3632276;
        return r3632277;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3632278 = z;
        double r3632279 = t;
        double r3632280 = x;
        double r3632281 = y;
        double r3632282 = c;
        double r3632283 = i;
        double r3632284 = b;
        double r3632285 = a;
        double r3632286 = r3632284 * r3632285;
        double r3632287 = fma(r3632282, r3632283, r3632286);
        double r3632288 = fma(r3632280, r3632281, r3632287);
        double r3632289 = fma(r3632278, r3632279, r3632288);
        return r3632289;
}

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 2019172 +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)))