Average Error: 0.0 → 0.0
Time: 16.7s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69895 = x;
        double r69896 = y;
        double r69897 = r69895 * r69896;
        double r69898 = z;
        double r69899 = t;
        double r69900 = r69898 * r69899;
        double r69901 = r69897 + r69900;
        double r69902 = a;
        double r69903 = b;
        double r69904 = r69902 * r69903;
        double r69905 = r69901 + r69904;
        double r69906 = c;
        double r69907 = i;
        double r69908 = r69906 * r69907;
        double r69909 = r69905 + r69908;
        return r69909;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69910 = c;
        double r69911 = i;
        double r69912 = a;
        double r69913 = b;
        double r69914 = x;
        double r69915 = y;
        double r69916 = z;
        double r69917 = t;
        double r69918 = r69916 * r69917;
        double r69919 = fma(r69914, r69915, r69918);
        double r69920 = fma(r69912, r69913, r69919);
        double r69921 = fma(r69910, r69911, r69920);
        return r69921;
}

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

Bits error versus i

Derivation

  1. Initial program 0.0

    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))