Average Error: 0.0 → 0.0
Time: 6.2s
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 r888484 = x;
        double r888485 = y;
        double r888486 = r888484 * r888485;
        double r888487 = z;
        double r888488 = t;
        double r888489 = r888487 * r888488;
        double r888490 = r888486 + r888489;
        double r888491 = a;
        double r888492 = b;
        double r888493 = r888491 * r888492;
        double r888494 = r888490 + r888493;
        double r888495 = c;
        double r888496 = i;
        double r888497 = r888495 * r888496;
        double r888498 = r888494 + r888497;
        return r888498;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r888499 = z;
        double r888500 = t;
        double r888501 = x;
        double r888502 = y;
        double r888503 = c;
        double r888504 = i;
        double r888505 = b;
        double r888506 = a;
        double r888507 = r888505 * r888506;
        double r888508 = fma(r888503, r888504, r888507);
        double r888509 = fma(r888501, r888502, r888508);
        double r888510 = fma(r888499, r888500, r888509);
        return r888510;
}

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 2019152 +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)))