Average Error: 0.1 → 0.0
Time: 10.8s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{-b}{4}, a, c\right)\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{-b}{4}, a, c\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r166611 = x;
        double r166612 = y;
        double r166613 = r166611 * r166612;
        double r166614 = z;
        double r166615 = t;
        double r166616 = r166614 * r166615;
        double r166617 = 16.0;
        double r166618 = r166616 / r166617;
        double r166619 = r166613 + r166618;
        double r166620 = a;
        double r166621 = b;
        double r166622 = r166620 * r166621;
        double r166623 = 4.0;
        double r166624 = r166622 / r166623;
        double r166625 = r166619 - r166624;
        double r166626 = c;
        double r166627 = r166625 + r166626;
        return r166627;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r166628 = t;
        double r166629 = z;
        double r166630 = 16.0;
        double r166631 = r166629 / r166630;
        double r166632 = x;
        double r166633 = y;
        double r166634 = b;
        double r166635 = -r166634;
        double r166636 = 4.0;
        double r166637 = r166635 / r166636;
        double r166638 = a;
        double r166639 = c;
        double r166640 = fma(r166637, r166638, r166639);
        double r166641 = fma(r166632, r166633, r166640);
        double r166642 = fma(r166628, r166631, r166641);
        return r166642;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{-b}{4}, a, c\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{-b}{4}, a, c\right)\right)\right)\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))