Average Error: 0.0 → 0.0
Time: 11.4s
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 r3460332 = x;
        double r3460333 = y;
        double r3460334 = r3460332 * r3460333;
        double r3460335 = z;
        double r3460336 = t;
        double r3460337 = r3460335 * r3460336;
        double r3460338 = r3460334 + r3460337;
        double r3460339 = a;
        double r3460340 = b;
        double r3460341 = r3460339 * r3460340;
        double r3460342 = r3460338 + r3460341;
        double r3460343 = c;
        double r3460344 = i;
        double r3460345 = r3460343 * r3460344;
        double r3460346 = r3460342 + r3460345;
        return r3460346;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3460347 = z;
        double r3460348 = t;
        double r3460349 = x;
        double r3460350 = y;
        double r3460351 = c;
        double r3460352 = i;
        double r3460353 = b;
        double r3460354 = a;
        double r3460355 = r3460353 * r3460354;
        double r3460356 = fma(r3460351, r3460352, r3460355);
        double r3460357 = fma(r3460349, r3460350, r3460356);
        double r3460358 = fma(r3460347, r3460348, r3460357);
        return r3460358;
}

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 2019169 +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)))