Jmat.Real.dawson

Average Error: 4.2 → 3.4

Time: 2.7m

Precision: 64

Math

\[\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(0.1049934947\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(0.0424060604\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0072644182\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0005064034\right) \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0001789971\right) \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(0.7715471019\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(0.2909738639\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0694555761\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0140005442\right) \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0008327945\right) \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(\left(2\right) \cdot \left(0.0001789971\right)\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}\right) \cdot x\]

↓

\[\frac{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(0.1049934947\right)}{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.0072644182\right)}{\left(\left(0.0005064034\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}{\left(0.0424060604\right)}\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}{\left(1\right)}\right) \cdot x\right)}{\left(\frac{\left(\frac{\left(\left(0.0140005442\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)}{\left(1\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right)\right)}{\left(0.0694555761\right)}\right)\right)}\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}\right)}\]

C

double f(double x) {
        double r5782843 = 1.0;
        double r5782844 = /* ERROR: no posit support in C */;
        double r5782845 = 0.1049934947;
        double r5782846 = /* ERROR: no posit support in C */;
        double r5782847 = x;
        double r5782848 = r5782847 * r5782847;
        double r5782849 = r5782846 * r5782848;
        double r5782850 = r5782844 + r5782849;
        double r5782851 = 0.0424060604;
        double r5782852 = /* ERROR: no posit support in C */;
        double r5782853 = r5782848 * r5782848;
        double r5782854 = r5782852 * r5782853;
        double r5782855 = r5782850 + r5782854;
        double r5782856 = 0.0072644182;
        double r5782857 = /* ERROR: no posit support in C */;
        double r5782858 = r5782853 * r5782848;
        double r5782859 = r5782857 * r5782858;
        double r5782860 = r5782855 + r5782859;
        double r5782861 = 0.0005064034;
        double r5782862 = /* ERROR: no posit support in C */;
        double r5782863 = r5782858 * r5782848;
        double r5782864 = r5782862 * r5782863;
        double r5782865 = r5782860 + r5782864;
        double r5782866 = 0.0001789971;
        double r5782867 = /* ERROR: no posit support in C */;
        double r5782868 = r5782863 * r5782848;
        double r5782869 = r5782867 * r5782868;
        double r5782870 = r5782865 + r5782869;
        double r5782871 = 0.7715471019;
        double r5782872 = /* ERROR: no posit support in C */;
        double r5782873 = r5782872 * r5782848;
        double r5782874 = r5782844 + r5782873;
        double r5782875 = 0.2909738639;
        double r5782876 = /* ERROR: no posit support in C */;
        double r5782877 = r5782876 * r5782853;
        double r5782878 = r5782874 + r5782877;
        double r5782879 = 0.0694555761;
        double r5782880 = /* ERROR: no posit support in C */;
        double r5782881 = r5782880 * r5782858;
        double r5782882 = r5782878 + r5782881;
        double r5782883 = 0.0140005442;
        double r5782884 = /* ERROR: no posit support in C */;
        double r5782885 = r5782884 * r5782863;
        double r5782886 = r5782882 + r5782885;
        double r5782887 = 0.0008327945;
        double r5782888 = /* ERROR: no posit support in C */;
        double r5782889 = r5782888 * r5782868;
        double r5782890 = r5782886 + r5782889;
        double r5782891 = 2.0;
        double r5782892 = /* ERROR: no posit support in C */;
        double r5782893 = r5782892 * r5782867;
        double r5782894 = r5782868 * r5782848;
        double r5782895 = r5782893 * r5782894;
        double r5782896 = r5782890 + r5782895;
        double r5782897 = r5782870 / r5782896;
        double r5782898 = r5782897 * r5782847;
        return r5782898;
}

↓

double f(double x) {
        double r5782899 = x;
        double r5782900 = r5782899 * r5782899;
        double r5782901 = 0.1049934947;
        double r5782902 = /* ERROR: no posit support in C */;
        double r5782903 = 0.0072644182;
        double r5782904 = /* ERROR: no posit support in C */;
        double r5782905 = 0.0005064034;
        double r5782906 = /* ERROR: no posit support in C */;
        double r5782907 = r5782906 * r5782900;
        double r5782908 = r5782904 + r5782907;
        double r5782909 = 0.0001789971;
        double r5782910 = /* ERROR: no posit support in C */;
        double r5782911 = r5782910 * r5782900;
        double r5782912 = r5782900 * r5782911;
        double r5782913 = r5782908 + r5782912;
        double r5782914 = r5782900 * r5782913;
        double r5782915 = 0.0424060604;
        double r5782916 = /* ERROR: no posit support in C */;
        double r5782917 = r5782914 + r5782916;
        double r5782918 = r5782917 * r5782900;
        double r5782919 = r5782902 + r5782918;
        double r5782920 = r5782900 * r5782919;
        double r5782921 = 1.0;
        double r5782922 = /* ERROR: no posit support in C */;
        double r5782923 = r5782920 + r5782922;
        double r5782924 = r5782923 * r5782899;
        double r5782925 = 0.0140005442;
        double r5782926 = /* ERROR: no posit support in C */;
        double r5782927 = r5782900 * r5782900;
        double r5782928 = r5782927 * r5782927;
        double r5782929 = r5782926 * r5782928;
        double r5782930 = r5782929 + r5782922;
        double r5782931 = 0.7715471019;
        double r5782932 = /* ERROR: no posit support in C */;
        double r5782933 = 2.0;
        double r5782934 = /* ERROR: no posit support in C */;
        double r5782935 = r5782911 * r5782934;
        double r5782936 = 0.0008327945;
        double r5782937 = /* ERROR: no posit support in C */;
        double r5782938 = r5782935 + r5782937;
        double r5782939 = r5782927 * r5782938;
        double r5782940 = 0.0694555761;
        double r5782941 = /* ERROR: no posit support in C */;
        double r5782942 = r5782939 + r5782941;
        double r5782943 = r5782927 * r5782942;
        double r5782944 = r5782932 + r5782943;
        double r5782945 = 0.2909738639;
        double r5782946 = /* ERROR: no posit support in C */;
        double r5782947 = r5782946 * r5782900;
        double r5782948 = r5782944 + r5782947;
        double r5782949 = r5782900 * r5782948;
        double r5782950 = r5782930 + r5782949;
        double r5782951 = r5782924 / r5782950;
        return r5782951;
}

Error

Bits error versus x

Derivation

1. Initial program 4.2

   \[\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(0.1049934947\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(0.0424060604\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0072644182\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0005064034\right) \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0001789971\right) \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(0.7715471019\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(0.2909738639\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0694555761\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0140005442\right) \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(0.0008327945\right) \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}{\left(\left(\left(2\right) \cdot \left(0.0001789971\right)\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}\right) \cdot x\]

2. Simplified 3.6

   \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}{\left(\frac{\left(0.0424060604\right)}{\left(\left(0.0072644182\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(0.1049934947\right)\right)}\right)}\right)}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(\frac{\left(\left(x \cdot x\right) \cdot \left(0.2909738639\right)\right)}{\left(0.7715471019\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761\right)\right)}\right)}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\frac{\left(0.0008327945\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(2\right)\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(0.0140005442\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)}\right)}\right) \cdot x}\]
3. Using strategy rm

4. Applied *p16-rgt-identity-expand 3.6

   \[\leadsto \left(\frac{\color{blue}{\left(\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}{\left(\frac{\left(0.0424060604\right)}{\left(\left(0.0072644182\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(0.1049934947\right)\right)}\right)}\right) \cdot \left(1.0\right)\right)}}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(\frac{\left(\left(x \cdot x\right) \cdot \left(0.2909738639\right)\right)}{\left(0.7715471019\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761\right)\right)}\right)}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\frac{\left(0.0008327945\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(2\right)\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(0.0140005442\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)}\right)}\right) \cdot x\]

5. Applied associate-/l* 3.6

   \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}{\left(\frac{\left(0.0424060604\right)}{\left(\left(0.0072644182\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(0.1049934947\right)\right)}\right)}\right)}{\left(\frac{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(\frac{\left(\left(x \cdot x\right) \cdot \left(0.2909738639\right)\right)}{\left(0.7715471019\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761\right)\right)}\right)}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\frac{\left(0.0008327945\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(2\right)\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(0.0140005442\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)}\right)}{\left(1.0\right)}\right)}\right)} \cdot x\]

6. Simplified 3.5

   \[\leadsto \left(\frac{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}{\left(\frac{\left(0.0424060604\right)}{\left(\left(0.0072644182\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(0.1049934947\right)\right)}\right)}\right)}{\color{blue}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0694555761\right)}{\left(\left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(\left(0.0140005442\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}}\right) \cdot x\]
7. Using strategy rm

8. Applied p16-*-un-lft-identity 3.5

   \[\leadsto \left(\frac{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}{\left(\frac{\left(0.0424060604\right)}{\left(\left(0.0072644182\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(0.1049934947\right)\right)}\right)}\right)}{\color{blue}{\left(\left(1.0\right) \cdot \left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0694555761\right)}{\left(\left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(\left(0.0140005442\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}}\right) \cdot x\]

9. Applied *p16-rgt-identity-expand 3.5

   \[\leadsto \left(\frac{\color{blue}{\left(\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}{\left(\frac{\left(0.0424060604\right)}{\left(\left(0.0072644182\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(0.1049934947\right)\right)}\right)}\right) \cdot \left(1.0\right)\right)}}{\left(\left(1.0\right) \cdot \left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0694555761\right)}{\left(\left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(\left(0.0140005442\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right) \cdot x\]

10. Applied p16-times-frac 3.5

    \[\leadsto \color{blue}{\left(\left(\frac{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}{\left(\frac{\left(0.0424060604\right)}{\left(\left(0.0072644182\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(0.1049934947\right)\right)}\right)}\right)}{\left(1.0\right)}\right) \cdot \left(\frac{\left(1.0\right)}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0694555761\right)}{\left(\left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(\left(0.0140005442\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}\right)\right)} \cdot x\]

11. Simplified 3.5

    \[\leadsto \left(\color{blue}{\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(\left(0.0001789971\right) \cdot x\right) \cdot x\right)}\right)\right)}{\left(0.0072644182\right)}\right)\right)}{\left(0.0424060604\right)}\right)\right)}{\left(0.1049934947\right)}\right)\right)}{\left(1\right)}\right)} \cdot \left(\frac{\left(1.0\right)}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0694555761\right)}{\left(\left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(\left(0.0140005442\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}\right)\right) \cdot x\]
12. Using strategy rm

13. Applied associate-*r/ 3.5

    \[\leadsto \color{blue}{\left(\frac{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(\left(0.0001789971\right) \cdot x\right) \cdot x\right)}\right)\right)}{\left(0.0072644182\right)}\right)\right)}{\left(0.0424060604\right)}\right)\right)}{\left(0.1049934947\right)}\right)\right)}{\left(1\right)}\right) \cdot \left(1.0\right)\right)}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0694555761\right)}{\left(\left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(\left(0.0140005442\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}\right)} \cdot x\]

14. Applied associate-*l/ 3.4

    \[\leadsto \color{blue}{\frac{\left(\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(\left(0.0001789971\right) \cdot x\right) \cdot x\right)}\right)\right)}{\left(0.0072644182\right)}\right)\right)}{\left(0.0424060604\right)}\right)\right)}{\left(0.1049934947\right)}\right)\right)}{\left(1\right)}\right) \cdot \left(1.0\right)\right) \cdot x\right)}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0694555761\right)}{\left(\left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(\left(0.0140005442\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}}\]

15. Simplified 3.3

    \[\leadsto \frac{\color{blue}{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(0.1049934947\right)}{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.0072644182\right)}{\left(\left(0.0005064034\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}{\left(0.0424060604\right)}\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}{\left(1\right)}\right) \cdot x\right)}}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0694555761\right)}{\left(\left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(\left(0.0140005442\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}\]
16. Using strategy rm

17. Applied /p16-rgt-identity-expand 3.3

    \[\leadsto \frac{\left(\color{blue}{\left(\frac{\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(0.1049934947\right)}{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.0072644182\right)}{\left(\left(0.0005064034\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}{\left(0.0424060604\right)}\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}{\left(1\right)}\right)}{\left(1.0\right)}\right)} \cdot x\right)}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0694555761\right)}{\left(\left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(\left(0.0140005442\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}\]

18. Applied associate-*l/ 3.3

    \[\leadsto \frac{\color{blue}{\left(\frac{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(0.1049934947\right)}{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.0072644182\right)}{\left(\left(0.0005064034\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}{\left(0.0424060604\right)}\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}{\left(1\right)}\right) \cdot x\right)}{\left(1.0\right)}\right)}}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0694555761\right)}{\left(\left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(\left(0.0140005442\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)}\]

19. Applied associate-/l/ 3.3

    \[\leadsto \color{blue}{\frac{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(0.1049934947\right)}{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.0072644182\right)}{\left(\left(0.0005064034\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}{\left(0.0424060604\right)}\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}{\left(1\right)}\right) \cdot x\right)}{\left(\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0694555761\right)}{\left(\left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(\left(0.0140005442\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}\right) \cdot \left(1.0\right)\right)}}\]

20. Simplified 3.4

    \[\leadsto \frac{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(0.1049934947\right)}{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.0072644182\right)}{\left(\left(0.0005064034\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}{\left(0.0424060604\right)}\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}{\left(1\right)}\right) \cdot x\right)}{\color{blue}{\left(\frac{\left(\frac{\left(\left(0.0140005442\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)}{\left(1\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right)\right)}{\left(0.0694555761\right)}\right)\right)}\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}\right)}}\]

21. Final simplification 3.4

    \[\leadsto \frac{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(0.1049934947\right)}{\left(\left(\frac{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.0072644182\right)}{\left(\left(0.0005064034\right) \cdot \left(x \cdot x\right)\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right)\right)}\right)\right)}{\left(0.0424060604\right)}\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}{\left(1\right)}\right) \cdot x\right)}{\left(\frac{\left(\frac{\left(\left(0.0140005442\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)}{\left(1\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(0.7715471019\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(2\right)\right)}{\left(0.0008327945\right)}\right)\right)}{\left(0.0694555761\right)}\right)\right)}\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}\right)}\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.dawson"
  (*.p16 (/.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.1049934947) (*.p16 x x))) (*.p16 (real->posit16 0.0424060604) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0072644182) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0005064034) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0001789971) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.7715471019) (*.p16 x x))) (*.p16 (real->posit16 0.2909738639) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0694555761) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0140005442) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0008327945) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (*.p16 (real->posit16 2) (real->posit16 0.0001789971)) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x))))) x))