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 r103987 = x;
        double r103988 = y;
        double r103989 = r103987 * r103988;
        double r103990 = z;
        double r103991 = t;
        double r103992 = r103990 * r103991;
        double r103993 = 16.0;
        double r103994 = r103992 / r103993;
        double r103995 = r103989 + r103994;
        double r103996 = a;
        double r103997 = b;
        double r103998 = r103996 * r103997;
        double r103999 = 4.0;
        double r104000 = r103998 / r103999;
        double r104001 = r103995 - r104000;
        double r104002 = c;
        double r104003 = r104001 + r104002;
        return r104003;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r104004 = z;
        double r104005 = 16.0;
        double r104006 = r104004 / r104005;
        double r104007 = t;
        double r104008 = x;
        double r104009 = y;
        double r104010 = a;
        double r104011 = 4.0;
        double r104012 = r104010 / r104011;
        double r104013 = b;
        double r104014 = -r104013;
        double r104015 = c;
        double r104016 = fma(r104012, r104014, r104015);
        double r104017 = fma(r104008, r104009, r104016);
        double r104018 = fma(r104006, r104007, r104017);
        return r104018;
}

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))