Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.1 → 29.2

Time: 7.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r65974 = x;
        double r65975 = y;
        double r65976 = r65974 * r65975;
        double r65977 = z;
        double r65978 = r65976 + r65977;
        double r65979 = r65978 * r65975;
        double r65980 = 27464.7644705;
        double r65981 = r65979 + r65980;
        double r65982 = r65981 * r65975;
        double r65983 = 230661.510616;
        double r65984 = r65982 + r65983;
        double r65985 = r65984 * r65975;
        double r65986 = t;
        double r65987 = r65985 + r65986;
        double r65988 = a;
        double r65989 = r65975 + r65988;
        double r65990 = r65989 * r65975;
        double r65991 = b;
        double r65992 = r65990 + r65991;
        double r65993 = r65992 * r65975;
        double r65994 = c;
        double r65995 = r65993 + r65994;
        double r65996 = r65995 * r65975;
        double r65997 = i;
        double r65998 = r65996 + r65997;
        double r65999 = r65987 / r65998;
        return r65999;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66000 = x;
        double r66001 = y;
        double r66002 = r66000 * r66001;
        double r66003 = z;
        double r66004 = r66002 + r66003;
        double r66005 = r66004 * r66001;
        double r66006 = cbrt(r66005);
        double r66007 = cbrt(r66006);
        double r66008 = r66007 * r66007;
        double r66009 = r66008 * r66007;
        double r66010 = r66009 * r66006;
        double r66011 = r66010 * r66006;
        double r66012 = 27464.7644705;
        double r66013 = r66011 + r66012;
        double r66014 = r66013 * r66001;
        double r66015 = 230661.510616;
        double r66016 = r66014 + r66015;
        double r66017 = r66016 * r66001;
        double r66018 = t;
        double r66019 = r66017 + r66018;
        double r66020 = a;
        double r66021 = r66001 + r66020;
        double r66022 = r66021 * r66001;
        double r66023 = b;
        double r66024 = r66022 + r66023;
        double r66025 = r66024 * r66001;
        double r66026 = c;
        double r66027 = r66025 + r66026;
        double r66028 = r66027 * r66001;
        double r66029 = i;
        double r66030 = r66028 + r66029;
        double r66031 = r66019 / r66030;
        return r66031;
}

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 29.1

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

3. Applied add-cube-cbrt 29.2

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

5. Applied add-cube-cbrt 29.2

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

6. Final simplification 29.2

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

Reproduce

herbie shell --seed 2020062 
(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)))