Average Error: 0.1 → 0.0
Time: 24.5s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
↓
\[\mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4.0}\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c
↓
\mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4.0}\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r11530982 = x;
        double r11530983 = y;
        double r11530984 = r11530982 * r11530983;
        double r11530985 = z;
        double r11530986 = t;
        double r11530987 = r11530985 * r11530986;
        double r11530988 = 16.0;
        double r11530989 = r11530987 / r11530988;
        double r11530990 = r11530984 + r11530989;
        double r11530991 = a;
        double r11530992 = b;
        double r11530993 = r11530991 * r11530992;
        double r11530994 = 4.0;
        double r11530995 = r11530993 / r11530994;
        double r11530996 = r11530990 - r11530995;
        double r11530997 = c;
        double r11530998 = r11530996 + r11530997;
        return r11530998;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r11530999 = t;
        double r11531000 = 16.0;
        double r11531001 = r11530999 / r11531000;
        double r11531002 = z;
        double r11531003 = y;
        double r11531004 = x;
        double r11531005 = c;
        double r11531006 = fma(r11531003, r11531004, r11531005);
        double r11531007 = b;
        double r11531008 = a;
        double r11531009 = r11531007 * r11531008;
        double r11531010 = 4.0;
        double r11531011 = r11531009 / r11531010;
        double r11531012 = r11531006 - r11531011;
        double r11531013 = fma(r11531001, r11531002, r11531012);
        return r11531013;
}

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

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{a \cdot b}{4.0}\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4.0}\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))