Average Error: 0.0 → 0.0
Time: 6.2s
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 r1719320 = x;
        double r1719321 = y;
        double r1719322 = r1719320 * r1719321;
        double r1719323 = z;
        double r1719324 = t;
        double r1719325 = r1719323 * r1719324;
        double r1719326 = r1719322 + r1719325;
        double r1719327 = a;
        double r1719328 = b;
        double r1719329 = r1719327 * r1719328;
        double r1719330 = r1719326 + r1719329;
        double r1719331 = c;
        double r1719332 = i;
        double r1719333 = r1719331 * r1719332;
        double r1719334 = r1719330 + r1719333;
        return r1719334;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1719335 = z;
        double r1719336 = t;
        double r1719337 = x;
        double r1719338 = y;
        double r1719339 = c;
        double r1719340 = i;
        double r1719341 = b;
        double r1719342 = a;
        double r1719343 = r1719341 * r1719342;
        double r1719344 = fma(r1719339, r1719340, r1719343);
        double r1719345 = fma(r1719337, r1719338, r1719344);
        double r1719346 = fma(r1719335, r1719336, r1719345);
        return r1719346;
}

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 2019144 +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)))