Average Error: 0.0 → 0.0
Time: 6.1s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2894921 = x;
        double r2894922 = y;
        double r2894923 = r2894921 * r2894922;
        double r2894924 = z;
        double r2894925 = t;
        double r2894926 = r2894924 * r2894925;
        double r2894927 = r2894923 + r2894926;
        double r2894928 = a;
        double r2894929 = b;
        double r2894930 = r2894928 * r2894929;
        double r2894931 = r2894927 + r2894930;
        double r2894932 = c;
        double r2894933 = i;
        double r2894934 = r2894932 * r2894933;
        double r2894935 = r2894931 + r2894934;
        return r2894935;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2894936 = z;
        double r2894937 = t;
        double r2894938 = x;
        double r2894939 = y;
        double r2894940 = c;
        double r2894941 = i;
        double r2894942 = b;
        double r2894943 = a;
        double r2894944 = r2894942 * r2894943;
        double r2894945 = fma(r2894940, r2894941, r2894944);
        double r2894946 = fma(r2894938, r2894939, r2894945);
        double r2894947 = fma(r2894936, r2894937, r2894946);
        return r2894947;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))