Average Error: 0.1 → 0.0
Time: 6.6s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{a}{4}, -b, c\right)\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{a}{4}, -b, c\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r143442 = x;
        double r143443 = y;
        double r143444 = r143442 * r143443;
        double r143445 = z;
        double r143446 = t;
        double r143447 = r143445 * r143446;
        double r143448 = 16.0;
        double r143449 = r143447 / r143448;
        double r143450 = r143444 + r143449;
        double r143451 = a;
        double r143452 = b;
        double r143453 = r143451 * r143452;
        double r143454 = 4.0;
        double r143455 = r143453 / r143454;
        double r143456 = r143450 - r143455;
        double r143457 = c;
        double r143458 = r143456 + r143457;
        return r143458;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r143459 = z;
        double r143460 = 16.0;
        double r143461 = r143459 / r143460;
        double r143462 = t;
        double r143463 = x;
        double r143464 = y;
        double r143465 = a;
        double r143466 = 4.0;
        double r143467 = r143465 / r143466;
        double r143468 = b;
        double r143469 = -r143468;
        double r143470 = c;
        double r143471 = fma(r143467, r143469, r143470);
        double r143472 = fma(r143463, r143464, r143471);
        double r143473 = fma(r143461, r143462, r143472);
        return r143473;
}

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

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{a}{4}, -b, c\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{a}{4}, -b, c\right)\right)\right)\]

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16)) (/ (* a b) 4)) c))