Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.1 → 29.2

Time: 9.2s

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 r60914 = x;
        double r60915 = y;
        double r60916 = r60914 * r60915;
        double r60917 = z;
        double r60918 = r60916 + r60917;
        double r60919 = r60918 * r60915;
        double r60920 = 27464.7644705;
        double r60921 = r60919 + r60920;
        double r60922 = r60921 * r60915;
        double r60923 = 230661.510616;
        double r60924 = r60922 + r60923;
        double r60925 = r60924 * r60915;
        double r60926 = t;
        double r60927 = r60925 + r60926;
        double r60928 = a;
        double r60929 = r60915 + r60928;
        double r60930 = r60929 * r60915;
        double r60931 = b;
        double r60932 = r60930 + r60931;
        double r60933 = r60932 * r60915;
        double r60934 = c;
        double r60935 = r60933 + r60934;
        double r60936 = r60935 * r60915;
        double r60937 = i;
        double r60938 = r60936 + r60937;
        double r60939 = r60927 / r60938;
        return r60939;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r60940 = x;
        double r60941 = y;
        double r60942 = r60940 * r60941;
        double r60943 = z;
        double r60944 = r60942 + r60943;
        double r60945 = r60944 * r60941;
        double r60946 = 27464.7644705;
        double r60947 = r60945 + r60946;
        double r60948 = cbrt(r60947);
        double r60949 = r60948 * r60948;
        double r60950 = r60948 * r60941;
        double r60951 = r60949 * r60950;
        double r60952 = 230661.510616;
        double r60953 = r60951 + r60952;
        double r60954 = r60953 * r60941;
        double r60955 = t;
        double r60956 = r60954 + r60955;
        double r60957 = a;
        double r60958 = r60941 + r60957;
        double r60959 = r60958 * r60941;
        double r60960 = b;
        double r60961 = r60959 + r60960;
        double r60962 = r60961 * r60941;
        double r60963 = c;
        double r60964 = r60962 + r60963;
        double r60965 = r60964 * r60941;
        double r60966 = i;
        double r60967 = r60965 + r60966;
        double r60968 = r60956 / r60967;
        return r60968;
}

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 2019362 
(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)))