Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.1 → 29.2

Time: 25.8s

Precision: 64

Math

\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

↓

\[\frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r56919 = x;
        double r56920 = y;
        double r56921 = r56919 * r56920;
        double r56922 = z;
        double r56923 = r56921 + r56922;
        double r56924 = r56923 * r56920;
        double r56925 = 27464.7644705;
        double r56926 = r56924 + r56925;
        double r56927 = r56926 * r56920;
        double r56928 = 230661.510616;
        double r56929 = r56927 + r56928;
        double r56930 = r56929 * r56920;
        double r56931 = t;
        double r56932 = r56930 + r56931;
        double r56933 = a;
        double r56934 = r56920 + r56933;
        double r56935 = r56934 * r56920;
        double r56936 = b;
        double r56937 = r56935 + r56936;
        double r56938 = r56937 * r56920;
        double r56939 = c;
        double r56940 = r56938 + r56939;
        double r56941 = r56940 * r56920;
        double r56942 = i;
        double r56943 = r56941 + r56942;
        double r56944 = r56932 / r56943;
        return r56944;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r56945 = x;
        double r56946 = y;
        double r56947 = r56945 * r56946;
        double r56948 = z;
        double r56949 = r56947 + r56948;
        double r56950 = r56949 * r56946;
        double r56951 = 27464.7644705;
        double r56952 = r56950 + r56951;
        double r56953 = cbrt(r56952);
        double r56954 = r56953 * r56953;
        double r56955 = r56953 * r56946;
        double r56956 = r56954 * r56955;
        double r56957 = 230661.510616;
        double r56958 = r56956 + r56957;
        double r56959 = r56958 * r56946;
        double r56960 = t;
        double r56961 = r56959 + r56960;
        double r56962 = a;
        double r56963 = r56946 + r56962;
        double r56964 = r56963 * r56946;
        double r56965 = b;
        double r56966 = r56964 + r56965;
        double r56967 = r56966 * r56946;
        double r56968 = c;
        double r56969 = r56967 + r56968;
        double r56970 = r56969 * r56946;
        double r56971 = i;
        double r56972 = r56970 + r56971;
        double r56973 = r56961 / r56972;
        return r56973;
}

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

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
2. Using strategy rm

3. Applied add-cube-cbrt 29.2

   \[\leadsto \frac{\left(\color{blue}{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right)} \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

4. Applied associate-*l* 29.2

   \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right)} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

5. Final simplification 29.2

   \[\leadsto \frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019294 
(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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))