Average Error: 0.1 → 0.0
Time: 9.9s
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 r231672 = x;
        double r231673 = y;
        double r231674 = r231672 * r231673;
        double r231675 = z;
        double r231676 = t;
        double r231677 = r231675 * r231676;
        double r231678 = 16.0;
        double r231679 = r231677 / r231678;
        double r231680 = r231674 + r231679;
        double r231681 = a;
        double r231682 = b;
        double r231683 = r231681 * r231682;
        double r231684 = 4.0;
        double r231685 = r231683 / r231684;
        double r231686 = r231680 - r231685;
        double r231687 = c;
        double r231688 = r231686 + r231687;
        return r231688;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r231689 = z;
        double r231690 = 16.0;
        double r231691 = r231689 / r231690;
        double r231692 = t;
        double r231693 = x;
        double r231694 = y;
        double r231695 = a;
        double r231696 = 4.0;
        double r231697 = r231695 / r231696;
        double r231698 = b;
        double r231699 = -r231698;
        double r231700 = c;
        double r231701 = fma(r231697, r231699, r231700);
        double r231702 = fma(r231693, r231694, r231701);
        double r231703 = fma(r231691, r231692, r231702);
        return r231703;
}

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 2019198 +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))