Average Error: 0.1 → 0.0
Time: 10.9s
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 r114900 = x;
        double r114901 = y;
        double r114902 = r114900 * r114901;
        double r114903 = z;
        double r114904 = t;
        double r114905 = r114903 * r114904;
        double r114906 = 16.0;
        double r114907 = r114905 / r114906;
        double r114908 = r114902 + r114907;
        double r114909 = a;
        double r114910 = b;
        double r114911 = r114909 * r114910;
        double r114912 = 4.0;
        double r114913 = r114911 / r114912;
        double r114914 = r114908 - r114913;
        double r114915 = c;
        double r114916 = r114914 + r114915;
        return r114916;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r114917 = z;
        double r114918 = 16.0;
        double r114919 = r114917 / r114918;
        double r114920 = t;
        double r114921 = x;
        double r114922 = y;
        double r114923 = a;
        double r114924 = 4.0;
        double r114925 = r114923 / r114924;
        double r114926 = b;
        double r114927 = -r114926;
        double r114928 = c;
        double r114929 = fma(r114925, r114927, r114928);
        double r114930 = fma(r114921, r114922, r114929);
        double r114931 = fma(r114919, r114920, r114930);
        return r114931;
}

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 2019303 +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))