Average Error: 0.1 → 0.0
Time: 15.6s
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 r163898 = x;
        double r163899 = y;
        double r163900 = r163898 * r163899;
        double r163901 = z;
        double r163902 = t;
        double r163903 = r163901 * r163902;
        double r163904 = 16.0;
        double r163905 = r163903 / r163904;
        double r163906 = r163900 + r163905;
        double r163907 = a;
        double r163908 = b;
        double r163909 = r163907 * r163908;
        double r163910 = 4.0;
        double r163911 = r163909 / r163910;
        double r163912 = r163906 - r163911;
        double r163913 = c;
        double r163914 = r163912 + r163913;
        return r163914;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r163915 = z;
        double r163916 = 16.0;
        double r163917 = r163915 / r163916;
        double r163918 = t;
        double r163919 = x;
        double r163920 = y;
        double r163921 = a;
        double r163922 = 4.0;
        double r163923 = r163921 / r163922;
        double r163924 = b;
        double r163925 = -r163924;
        double r163926 = c;
        double r163927 = fma(r163923, r163925, r163926);
        double r163928 = fma(r163919, r163920, r163927);
        double r163929 = fma(r163917, r163918, r163928);
        return r163929;
}

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 2019209 +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))