Average Error: 0.0 → 0.0
Time: 6.4s
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 r106386 = x;
        double r106387 = y;
        double r106388 = r106386 * r106387;
        double r106389 = z;
        double r106390 = t;
        double r106391 = r106389 * r106390;
        double r106392 = r106388 + r106391;
        double r106393 = a;
        double r106394 = b;
        double r106395 = r106393 * r106394;
        double r106396 = r106392 + r106395;
        double r106397 = c;
        double r106398 = i;
        double r106399 = r106397 * r106398;
        double r106400 = r106396 + r106399;
        return r106400;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r106401 = c;
        double r106402 = i;
        double r106403 = a;
        double r106404 = b;
        double r106405 = x;
        double r106406 = y;
        double r106407 = z;
        double r106408 = t;
        double r106409 = r106407 * r106408;
        double r106410 = fma(r106405, r106406, r106409);
        double r106411 = fma(r106403, r106404, r106410);
        double r106412 = fma(r106401, r106402, r106411);
        return r106412;
}

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 2019199 +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)))