Average Error: 28.9 → 28.9
Time: 8.7s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}\]
\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot 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) \cdot 1}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80949 = x;
        double r80950 = y;
        double r80951 = r80949 * r80950;
        double r80952 = z;
        double r80953 = r80951 + r80952;
        double r80954 = r80953 * r80950;
        double r80955 = 27464.7644705;
        double r80956 = r80954 + r80955;
        double r80957 = r80956 * r80950;
        double r80958 = 230661.510616;
        double r80959 = r80957 + r80958;
        double r80960 = r80959 * r80950;
        double r80961 = t;
        double r80962 = r80960 + r80961;
        double r80963 = a;
        double r80964 = r80950 + r80963;
        double r80965 = r80964 * r80950;
        double r80966 = b;
        double r80967 = r80965 + r80966;
        double r80968 = r80967 * r80950;
        double r80969 = c;
        double r80970 = r80968 + r80969;
        double r80971 = r80970 * r80950;
        double r80972 = i;
        double r80973 = r80971 + r80972;
        double r80974 = r80962 / r80973;
        return r80974;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80975 = x;
        double r80976 = y;
        double r80977 = r80975 * r80976;
        double r80978 = z;
        double r80979 = r80977 + r80978;
        double r80980 = r80979 * r80976;
        double r80981 = 27464.7644705;
        double r80982 = r80980 + r80981;
        double r80983 = r80982 * r80976;
        double r80984 = 230661.510616;
        double r80985 = r80983 + r80984;
        double r80986 = r80985 * r80976;
        double r80987 = t;
        double r80988 = r80986 + r80987;
        double r80989 = 1.0;
        double r80990 = a;
        double r80991 = r80976 + r80990;
        double r80992 = b;
        double r80993 = fma(r80991, r80976, r80992);
        double r80994 = c;
        double r80995 = fma(r80993, r80976, r80994);
        double r80996 = i;
        double r80997 = fma(r80995, r80976, r80996);
        double r80998 = r80997 * r80989;
        double r80999 = r80989 / r80998;
        double r81000 = r80988 * r80999;
        return r81000;
}

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 28.9

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

  3. Applied div-inv28.9

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

  4. Simplified28.9

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

  5. Final simplification28.9

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))