Average Error: 0.1 → 0.0
Time: 5.6s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(z, \frac{t}{16}, \mathsf{fma}\left(y, x, \mathsf{fma}\left(-\frac{a}{4}, b, c\right)\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(z, \frac{t}{16}, \mathsf{fma}\left(y, x, \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 r208567 = x;
        double r208568 = y;
        double r208569 = r208567 * r208568;
        double r208570 = z;
        double r208571 = t;
        double r208572 = r208570 * r208571;
        double r208573 = 16.0;
        double r208574 = r208572 / r208573;
        double r208575 = r208569 + r208574;
        double r208576 = a;
        double r208577 = b;
        double r208578 = r208576 * r208577;
        double r208579 = 4.0;
        double r208580 = r208578 / r208579;
        double r208581 = r208575 - r208580;
        double r208582 = c;
        double r208583 = r208581 + r208582;
        return r208583;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r208584 = z;
        double r208585 = t;
        double r208586 = 16.0;
        double r208587 = r208585 / r208586;
        double r208588 = y;
        double r208589 = x;
        double r208590 = a;
        double r208591 = 4.0;
        double r208592 = r208590 / r208591;
        double r208593 = -r208592;
        double r208594 = b;
        double r208595 = c;
        double r208596 = fma(r208593, r208594, r208595);
        double r208597 = fma(r208588, r208589, r208596);
        double r208598 = fma(r208584, r208587, r208597);
        return r208598;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +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))