Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, x \cdot y + z \cdot t\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, x \cdot y + z \cdot t\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r149920 = x;
        double r149921 = y;
        double r149922 = r149920 * r149921;
        double r149923 = z;
        double r149924 = t;
        double r149925 = r149923 * r149924;
        double r149926 = r149922 + r149925;
        double r149927 = a;
        double r149928 = b;
        double r149929 = r149927 * r149928;
        double r149930 = r149926 + r149929;
        double r149931 = c;
        double r149932 = i;
        double r149933 = r149931 * r149932;
        double r149934 = r149930 + r149933;
        return r149934;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r149935 = i;
        double r149936 = c;
        double r149937 = b;
        double r149938 = a;
        double r149939 = x;
        double r149940 = y;
        double r149941 = r149939 * r149940;
        double r149942 = z;
        double r149943 = t;
        double r149944 = r149942 * r149943;
        double r149945 = r149941 + r149944;
        double r149946 = fma(r149937, r149938, r149945);
        double r149947 = fma(r149935, r149936, r149946);
        return r149947;
}

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

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

  4. Applied fma-udef0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))