Average Error: 0.1 → 0.0
Time: 6.1s
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 r191355 = x;
        double r191356 = y;
        double r191357 = r191355 * r191356;
        double r191358 = z;
        double r191359 = t;
        double r191360 = r191358 * r191359;
        double r191361 = 16.0;
        double r191362 = r191360 / r191361;
        double r191363 = r191357 + r191362;
        double r191364 = a;
        double r191365 = b;
        double r191366 = r191364 * r191365;
        double r191367 = 4.0;
        double r191368 = r191366 / r191367;
        double r191369 = r191363 - r191368;
        double r191370 = c;
        double r191371 = r191369 + r191370;
        return r191371;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r191372 = z;
        double r191373 = 16.0;
        double r191374 = r191372 / r191373;
        double r191375 = t;
        double r191376 = x;
        double r191377 = y;
        double r191378 = a;
        double r191379 = 4.0;
        double r191380 = r191378 / r191379;
        double r191381 = b;
        double r191382 = -r191381;
        double r191383 = c;
        double r191384 = fma(r191380, r191382, r191383);
        double r191385 = fma(r191376, r191377, r191384);
        double r191386 = fma(r191374, r191375, r191385);
        return r191386;
}

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))