Average Error: 0.1 → 0.0
Time: 6.8s
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 r136615 = x;
        double r136616 = y;
        double r136617 = r136615 * r136616;
        double r136618 = z;
        double r136619 = t;
        double r136620 = r136618 * r136619;
        double r136621 = 16.0;
        double r136622 = r136620 / r136621;
        double r136623 = r136617 + r136622;
        double r136624 = a;
        double r136625 = b;
        double r136626 = r136624 * r136625;
        double r136627 = 4.0;
        double r136628 = r136626 / r136627;
        double r136629 = r136623 - r136628;
        double r136630 = c;
        double r136631 = r136629 + r136630;
        return r136631;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r136632 = z;
        double r136633 = 16.0;
        double r136634 = r136632 / r136633;
        double r136635 = t;
        double r136636 = x;
        double r136637 = y;
        double r136638 = a;
        double r136639 = 4.0;
        double r136640 = r136638 / r136639;
        double r136641 = b;
        double r136642 = -r136641;
        double r136643 = c;
        double r136644 = fma(r136640, r136642, r136643);
        double r136645 = fma(r136636, r136637, r136644);
        double r136646 = fma(r136634, r136635, r136645);
        return r136646;
}

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 2019306 +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))