Average Error: 0.0 → 0.0
Time: 9.1s
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 r4146384 = x;
        double r4146385 = y;
        double r4146386 = r4146384 * r4146385;
        double r4146387 = z;
        double r4146388 = t;
        double r4146389 = r4146387 * r4146388;
        double r4146390 = r4146386 + r4146389;
        double r4146391 = a;
        double r4146392 = b;
        double r4146393 = r4146391 * r4146392;
        double r4146394 = r4146390 + r4146393;
        double r4146395 = c;
        double r4146396 = i;
        double r4146397 = r4146395 * r4146396;
        double r4146398 = r4146394 + r4146397;
        return r4146398;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4146399 = z;
        double r4146400 = t;
        double r4146401 = x;
        double r4146402 = y;
        double r4146403 = c;
        double r4146404 = i;
        double r4146405 = b;
        double r4146406 = a;
        double r4146407 = r4146405 * r4146406;
        double r4146408 = fma(r4146403, r4146404, r4146407);
        double r4146409 = fma(r4146401, r4146402, r4146408);
        double r4146410 = fma(r4146399, r4146400, r4146409);
        return r4146410;
}

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 2019168 +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)))