Average Error: 0.0 → 0.0
Time: 9.3s
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 r64313 = x;
        double r64314 = y;
        double r64315 = r64313 * r64314;
        double r64316 = z;
        double r64317 = t;
        double r64318 = r64316 * r64317;
        double r64319 = r64315 + r64318;
        double r64320 = a;
        double r64321 = b;
        double r64322 = r64320 * r64321;
        double r64323 = r64319 + r64322;
        double r64324 = c;
        double r64325 = i;
        double r64326 = r64324 * r64325;
        double r64327 = r64323 + r64326;
        return r64327;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r64328 = c;
        double r64329 = i;
        double r64330 = a;
        double r64331 = b;
        double r64332 = x;
        double r64333 = y;
        double r64334 = z;
        double r64335 = t;
        double r64336 = r64334 * r64335;
        double r64337 = fma(r64332, r64333, r64336);
        double r64338 = fma(r64330, r64331, r64337);
        double r64339 = fma(r64328, r64329, r64338);
        return r64339;
}

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, C"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))