Average Error: 0.1 → 0.0
Time: 6.5s
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 r208413 = x;
        double r208414 = y;
        double r208415 = r208413 * r208414;
        double r208416 = z;
        double r208417 = t;
        double r208418 = r208416 * r208417;
        double r208419 = 16.0;
        double r208420 = r208418 / r208419;
        double r208421 = r208415 + r208420;
        double r208422 = a;
        double r208423 = b;
        double r208424 = r208422 * r208423;
        double r208425 = 4.0;
        double r208426 = r208424 / r208425;
        double r208427 = r208421 - r208426;
        double r208428 = c;
        double r208429 = r208427 + r208428;
        return r208429;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r208430 = z;
        double r208431 = 16.0;
        double r208432 = r208430 / r208431;
        double r208433 = t;
        double r208434 = x;
        double r208435 = y;
        double r208436 = a;
        double r208437 = 4.0;
        double r208438 = r208436 / r208437;
        double r208439 = b;
        double r208440 = -r208439;
        double r208441 = c;
        double r208442 = fma(r208438, r208440, r208441);
        double r208443 = fma(r208434, r208435, r208442);
        double r208444 = fma(r208432, r208433, r208443);
        return r208444;
}

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 2020047 +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))