Average Error: 0.2 → 0.0
Time: 4.6s
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 r149419 = x;
        double r149420 = y;
        double r149421 = r149419 * r149420;
        double r149422 = z;
        double r149423 = t;
        double r149424 = r149422 * r149423;
        double r149425 = 16.0;
        double r149426 = r149424 / r149425;
        double r149427 = r149421 + r149426;
        double r149428 = a;
        double r149429 = b;
        double r149430 = r149428 * r149429;
        double r149431 = 4.0;
        double r149432 = r149430 / r149431;
        double r149433 = r149427 - r149432;
        double r149434 = c;
        double r149435 = r149433 + r149434;
        return r149435;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r149436 = z;
        double r149437 = 16.0;
        double r149438 = r149436 / r149437;
        double r149439 = t;
        double r149440 = x;
        double r149441 = y;
        double r149442 = a;
        double r149443 = 4.0;
        double r149444 = r149442 / r149443;
        double r149445 = b;
        double r149446 = -r149445;
        double r149447 = c;
        double r149448 = fma(r149444, r149446, r149447);
        double r149449 = fma(r149440, r149441, r149448);
        double r149450 = fma(r149438, r149439, r149449);
        return r149450;
}

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 0.2

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

  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 2019208 +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))