Average Error: 0.1 → 0.0
Time: 3.7s
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 r235613 = x;
        double r235614 = y;
        double r235615 = r235613 * r235614;
        double r235616 = z;
        double r235617 = t;
        double r235618 = r235616 * r235617;
        double r235619 = 16.0;
        double r235620 = r235618 / r235619;
        double r235621 = r235615 + r235620;
        double r235622 = a;
        double r235623 = b;
        double r235624 = r235622 * r235623;
        double r235625 = 4.0;
        double r235626 = r235624 / r235625;
        double r235627 = r235621 - r235626;
        double r235628 = c;
        double r235629 = r235627 + r235628;
        return r235629;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r235630 = z;
        double r235631 = 16.0;
        double r235632 = r235630 / r235631;
        double r235633 = t;
        double r235634 = x;
        double r235635 = y;
        double r235636 = a;
        double r235637 = 4.0;
        double r235638 = r235636 / r235637;
        double r235639 = b;
        double r235640 = -r235639;
        double r235641 = c;
        double r235642 = fma(r235638, r235640, r235641);
        double r235643 = fma(r235634, r235635, r235642);
        double r235644 = fma(r235632, r235633, r235643);
        return r235644;
}

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 2020043 +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))