Average Error: 0.1 → 0.0
Time: 6.0s
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 r128684 = x;
        double r128685 = y;
        double r128686 = r128684 * r128685;
        double r128687 = z;
        double r128688 = t;
        double r128689 = r128687 * r128688;
        double r128690 = 16.0;
        double r128691 = r128689 / r128690;
        double r128692 = r128686 + r128691;
        double r128693 = a;
        double r128694 = b;
        double r128695 = r128693 * r128694;
        double r128696 = 4.0;
        double r128697 = r128695 / r128696;
        double r128698 = r128692 - r128697;
        double r128699 = c;
        double r128700 = r128698 + r128699;
        return r128700;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r128701 = z;
        double r128702 = 16.0;
        double r128703 = r128701 / r128702;
        double r128704 = t;
        double r128705 = x;
        double r128706 = y;
        double r128707 = a;
        double r128708 = 4.0;
        double r128709 = r128707 / r128708;
        double r128710 = b;
        double r128711 = -r128710;
        double r128712 = c;
        double r128713 = fma(r128709, r128711, r128712);
        double r128714 = fma(r128705, r128706, r128713);
        double r128715 = fma(r128703, r128704, r128714);
        return r128715;
}

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 2019212 +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))