Average Error: 0.1 → 0.0
Time: 7.3s
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 r163812 = x;
        double r163813 = y;
        double r163814 = r163812 * r163813;
        double r163815 = z;
        double r163816 = t;
        double r163817 = r163815 * r163816;
        double r163818 = 16.0;
        double r163819 = r163817 / r163818;
        double r163820 = r163814 + r163819;
        double r163821 = a;
        double r163822 = b;
        double r163823 = r163821 * r163822;
        double r163824 = 4.0;
        double r163825 = r163823 / r163824;
        double r163826 = r163820 - r163825;
        double r163827 = c;
        double r163828 = r163826 + r163827;
        return r163828;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r163829 = z;
        double r163830 = 16.0;
        double r163831 = r163829 / r163830;
        double r163832 = t;
        double r163833 = x;
        double r163834 = y;
        double r163835 = a;
        double r163836 = 4.0;
        double r163837 = r163835 / r163836;
        double r163838 = b;
        double r163839 = -r163838;
        double r163840 = c;
        double r163841 = fma(r163837, r163839, r163840);
        double r163842 = fma(r163833, r163834, r163841);
        double r163843 = fma(r163831, r163832, r163842);
        return r163843;
}

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 2019323 +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))