Average Error: 29.0 → 29.1
Time: 47.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.764470499998\right), y, 230661.510616000014\right), y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.764470499998\right), y, 230661.510616000014\right), y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r65917 = x;
        double r65918 = y;
        double r65919 = r65917 * r65918;
        double r65920 = z;
        double r65921 = r65919 + r65920;
        double r65922 = r65921 * r65918;
        double r65923 = 27464.7644705;
        double r65924 = r65922 + r65923;
        double r65925 = r65924 * r65918;
        double r65926 = 230661.510616;
        double r65927 = r65925 + r65926;
        double r65928 = r65927 * r65918;
        double r65929 = t;
        double r65930 = r65928 + r65929;
        double r65931 = a;
        double r65932 = r65918 + r65931;
        double r65933 = r65932 * r65918;
        double r65934 = b;
        double r65935 = r65933 + r65934;
        double r65936 = r65935 * r65918;
        double r65937 = c;
        double r65938 = r65936 + r65937;
        double r65939 = r65938 * r65918;
        double r65940 = i;
        double r65941 = r65939 + r65940;
        double r65942 = r65930 / r65941;
        return r65942;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r65943 = x;
        double r65944 = y;
        double r65945 = z;
        double r65946 = fma(r65943, r65944, r65945);
        double r65947 = 27464.7644705;
        double r65948 = fma(r65946, r65944, r65947);
        double r65949 = 230661.510616;
        double r65950 = fma(r65948, r65944, r65949);
        double r65951 = t;
        double r65952 = fma(r65950, r65944, r65951);
        double r65953 = 1.0;
        double r65954 = a;
        double r65955 = r65944 + r65954;
        double r65956 = b;
        double r65957 = fma(r65955, r65944, r65956);
        double r65958 = c;
        double r65959 = fma(r65957, r65944, r65958);
        double r65960 = i;
        double r65961 = fma(r65959, r65944, r65960);
        double r65962 = r65953 / r65961;
        double r65963 = r65952 * r65962;
        return r65963;
}

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 29.0

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified29.0

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.764470499998\right), y, 230661.510616000014\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}}\]
  3. Using strategy rm

  4. Applied div-inv29.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.764470499998\right), y, 230661.510616000014\right), y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}}\]

  5. Final simplification29.1

    \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.764470499998\right), y, 230661.510616000014\right), y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))