Average Error: 0.0 → 0.0
Time: 4.4s
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 r2466321 = x;
        double r2466322 = y;
        double r2466323 = r2466321 * r2466322;
        double r2466324 = z;
        double r2466325 = t;
        double r2466326 = r2466324 * r2466325;
        double r2466327 = r2466323 + r2466326;
        double r2466328 = a;
        double r2466329 = b;
        double r2466330 = r2466328 * r2466329;
        double r2466331 = r2466327 + r2466330;
        double r2466332 = c;
        double r2466333 = i;
        double r2466334 = r2466332 * r2466333;
        double r2466335 = r2466331 + r2466334;
        return r2466335;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2466336 = z;
        double r2466337 = t;
        double r2466338 = x;
        double r2466339 = y;
        double r2466340 = c;
        double r2466341 = i;
        double r2466342 = b;
        double r2466343 = a;
        double r2466344 = r2466342 * r2466343;
        double r2466345 = fma(r2466340, r2466341, r2466344);
        double r2466346 = fma(r2466338, r2466339, r2466345);
        double r2466347 = fma(r2466336, r2466337, r2466346);
        return r2466347;
}

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 2019156 +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)))