Average Error: 28.7 → 28.8
Time: 15.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]
\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}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69956 = x;
        double r69957 = y;
        double r69958 = r69956 * r69957;
        double r69959 = z;
        double r69960 = r69958 + r69959;
        double r69961 = r69960 * r69957;
        double r69962 = 27464.7644705;
        double r69963 = r69961 + r69962;
        double r69964 = r69963 * r69957;
        double r69965 = 230661.510616;
        double r69966 = r69964 + r69965;
        double r69967 = r69966 * r69957;
        double r69968 = t;
        double r69969 = r69967 + r69968;
        double r69970 = a;
        double r69971 = r69957 + r69970;
        double r69972 = r69971 * r69957;
        double r69973 = b;
        double r69974 = r69972 + r69973;
        double r69975 = r69974 * r69957;
        double r69976 = c;
        double r69977 = r69975 + r69976;
        double r69978 = r69977 * r69957;
        double r69979 = i;
        double r69980 = r69978 + r69979;
        double r69981 = r69969 / r69980;
        return r69981;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69982 = x;
        double r69983 = y;
        double r69984 = r69982 * r69983;
        double r69985 = z;
        double r69986 = r69984 + r69985;
        double r69987 = r69986 * r69983;
        double r69988 = 27464.7644705;
        double r69989 = r69987 + r69988;
        double r69990 = r69989 * r69983;
        double r69991 = 230661.510616;
        double r69992 = r69990 + r69991;
        double r69993 = r69992 * r69983;
        double r69994 = t;
        double r69995 = r69993 + r69994;
        double r69996 = 1.0;
        double r69997 = b;
        double r69998 = r69983 * r69997;
        double r69999 = 3.0;
        double r70000 = pow(r69983, r69999);
        double r70001 = a;
        double r70002 = 2.0;
        double r70003 = pow(r69983, r70002);
        double r70004 = r70001 * r70003;
        double r70005 = r70000 + r70004;
        double r70006 = r69998 + r70005;
        double r70007 = c;
        double r70008 = r70006 + r70007;
        double r70009 = r70008 * r69983;
        double r70010 = i;
        double r70011 = r70009 + r70010;
        double r70012 = r69996 / r70011;
        double r70013 = r69995 * r70012;
        return r70013;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 28.7

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

  2. Taylor expanded around inf 28.7

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right)} + c\right) \cdot y + i}\]
  3. Using strategy rm

  4. Applied div-inv28.8

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}}\]

  5. Final simplification28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020047 
(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)))