Average Error: 0.2 → 0.0
Time: 9.8s
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 r235361 = x;
        double r235362 = y;
        double r235363 = r235361 * r235362;
        double r235364 = z;
        double r235365 = t;
        double r235366 = r235364 * r235365;
        double r235367 = 16.0;
        double r235368 = r235366 / r235367;
        double r235369 = r235363 + r235368;
        double r235370 = a;
        double r235371 = b;
        double r235372 = r235370 * r235371;
        double r235373 = 4.0;
        double r235374 = r235372 / r235373;
        double r235375 = r235369 - r235374;
        double r235376 = c;
        double r235377 = r235375 + r235376;
        return r235377;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r235378 = z;
        double r235379 = 16.0;
        double r235380 = r235378 / r235379;
        double r235381 = t;
        double r235382 = x;
        double r235383 = y;
        double r235384 = a;
        double r235385 = 4.0;
        double r235386 = r235384 / r235385;
        double r235387 = b;
        double r235388 = -r235387;
        double r235389 = c;
        double r235390 = fma(r235386, r235388, r235389);
        double r235391 = fma(r235382, r235383, r235390);
        double r235392 = fma(r235380, r235381, r235391);
        return r235392;
}

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 2020042 +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))