Average Error: 27.9 → 28.1
Time: 36.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2014955 = x;
        double r2014956 = y;
        double r2014957 = r2014955 * r2014956;
        double r2014958 = z;
        double r2014959 = r2014957 + r2014958;
        double r2014960 = r2014959 * r2014956;
        double r2014961 = 27464.7644705;
        double r2014962 = r2014960 + r2014961;
        double r2014963 = r2014962 * r2014956;
        double r2014964 = 230661.510616;
        double r2014965 = r2014963 + r2014964;
        double r2014966 = r2014965 * r2014956;
        double r2014967 = t;
        double r2014968 = r2014966 + r2014967;
        double r2014969 = a;
        double r2014970 = r2014956 + r2014969;
        double r2014971 = r2014970 * r2014956;
        double r2014972 = b;
        double r2014973 = r2014971 + r2014972;
        double r2014974 = r2014973 * r2014956;
        double r2014975 = c;
        double r2014976 = r2014974 + r2014975;
        double r2014977 = r2014976 * r2014956;
        double r2014978 = i;
        double r2014979 = r2014977 + r2014978;
        double r2014980 = r2014968 / r2014979;
        return r2014980;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2014981 = 1.0;
        double r2014982 = y;
        double r2014983 = a;
        double r2014984 = r2014982 + r2014983;
        double r2014985 = b;
        double r2014986 = fma(r2014984, r2014982, r2014985);
        double r2014987 = c;
        double r2014988 = fma(r2014982, r2014986, r2014987);
        double r2014989 = i;
        double r2014990 = fma(r2014988, r2014982, r2014989);
        double r2014991 = x;
        double r2014992 = z;
        double r2014993 = fma(r2014982, r2014991, r2014992);
        double r2014994 = 27464.7644705;
        double r2014995 = fma(r2014982, r2014993, r2014994);
        double r2014996 = 230661.510616;
        double r2014997 = fma(r2014982, r2014995, r2014996);
        double r2014998 = t;
        double r2014999 = fma(r2014982, r2014997, r2014998);
        double r2015000 = r2014990 / r2014999;
        double r2015001 = r2014981 / r2015000;
        return r2015001;
}

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 27.9

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified27.9

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}}\]
  3. Using strategy rm

  4. Applied clear-num28.1

    \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}}\]

  5. Final simplification28.1

    \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}\]

Reproduce

herbie shell --seed 2019158 +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)))