Jmat.Real.dawson

Average Error: 4.3 → 3.5

Time: 1.8m

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\]

↓

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

C

double f(double x) {
        double r5747974 = 1.0;
        double r5747975 = /* ERROR: no posit support in C */;
        double r5747976 = 0.1049934947;
        double r5747977 = /* ERROR: no posit support in C */;
        double r5747978 = x;
        double r5747979 = r5747978 * r5747978;
        double r5747980 = r5747977 * r5747979;
        double r5747981 = r5747975 + r5747980;
        double r5747982 = 0.0424060604;
        double r5747983 = /* ERROR: no posit support in C */;
        double r5747984 = r5747979 * r5747979;
        double r5747985 = r5747983 * r5747984;
        double r5747986 = r5747981 + r5747985;
        double r5747987 = 0.0072644182;
        double r5747988 = /* ERROR: no posit support in C */;
        double r5747989 = r5747984 * r5747979;
        double r5747990 = r5747988 * r5747989;
        double r5747991 = r5747986 + r5747990;
        double r5747992 = 0.0005064034;
        double r5747993 = /* ERROR: no posit support in C */;
        double r5747994 = r5747989 * r5747979;
        double r5747995 = r5747993 * r5747994;
        double r5747996 = r5747991 + r5747995;
        double r5747997 = 0.0001789971;
        double r5747998 = /* ERROR: no posit support in C */;
        double r5747999 = r5747994 * r5747979;
        double r5748000 = r5747998 * r5747999;
        double r5748001 = r5747996 + r5748000;
        double r5748002 = 0.7715471019;
        double r5748003 = /* ERROR: no posit support in C */;
        double r5748004 = r5748003 * r5747979;
        double r5748005 = r5747975 + r5748004;
        double r5748006 = 0.2909738639;
        double r5748007 = /* ERROR: no posit support in C */;
        double r5748008 = r5748007 * r5747984;
        double r5748009 = r5748005 + r5748008;
        double r5748010 = 0.0694555761;
        double r5748011 = /* ERROR: no posit support in C */;
        double r5748012 = r5748011 * r5747989;
        double r5748013 = r5748009 + r5748012;
        double r5748014 = 0.0140005442;
        double r5748015 = /* ERROR: no posit support in C */;
        double r5748016 = r5748015 * r5747994;
        double r5748017 = r5748013 + r5748016;
        double r5748018 = 0.0008327945;
        double r5748019 = /* ERROR: no posit support in C */;
        double r5748020 = r5748019 * r5747999;
        double r5748021 = r5748017 + r5748020;
        double r5748022 = 2.0;
        double r5748023 = /* ERROR: no posit support in C */;
        double r5748024 = r5748023 * r5747998;
        double r5748025 = r5747999 * r5747979;
        double r5748026 = r5748024 * r5748025;
        double r5748027 = r5748021 + r5748026;
        double r5748028 = r5748001 / r5748027;
        double r5748029 = r5748028 * r5747978;
        return r5748029;
}

↓

double f(double x) {
        double r5748030 = x;
        double r5748031 = r5748030 * r5748030;
        double r5748032 = r5748031 * r5748031;
        double r5748033 = 0.0005064034;
        double r5748034 = 0.0001789971;
        double r5748035 = r5748034 * r5748030;
        double r5748036 = r5748030 * r5748035;
        double r5748037 = r5748033 + r5748036;
        double r5748038 = r5748031 * r5748037;
        double r5748039 = r5748031 * r5748038;
        double r5748040 = 0.0424060604;
        double r5748041 = 0.0072644182;
        double r5748042 = r5748041 * r5748031;
        double r5748043 = r5748040 + r5748042;
        double r5748044 = r5748039 + r5748043;
        double r5748045 = r5748032 * r5748044;
        double r5748046 = 1.0;
        double r5748047 = 0.1049934947;
        double r5748048 = r5748031 * r5748047;
        double r5748049 = r5748046 + r5748048;
        double r5748050 = r5748045 + r5748049;
        double r5748051 = 0.7715471019;
        double r5748052 = 0.2909738639;
        double r5748053 = r5748052 * r5748031;
        double r5748054 = r5748051 + r5748053;
        double r5748055 = 0.0694555761;
        double r5748056 = r5748035 * r5748030;
        double r5748057 = 2.0;
        double r5748058 = r5748056 * r5748057;
        double r5748059 = 0.0008327945;
        double r5748060 = r5748058 + r5748059;
        double r5748061 = r5748060 * r5748032;
        double r5748062 = r5748055 + r5748061;
        double r5748063 = r5748032 * r5748062;
        double r5748064 = r5748054 + r5748063;
        double r5748065 = r5748031 * r5748064;
        double r5748066 = r5748046 + r5748065;
        double r5748067 = 0.0140005442;
        double r5748068 = r5748067 * r5748032;
        double r5748069 = r5748068 * r5748032;
        double r5748070 = r5748066 + r5748069;
        double r5748071 = r5748050 / r5748070;
        double r5748072 = r5748071 * r5748030;
        return r5748072;
}

Error

Bits error versus x

Derivation

1. Initial program 4.3

   \[\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 associate-*r* 3.5

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

10. Applied associate-*l* 3.5

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

11. Simplified 3.5

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

13. Applied associate-*l* 3.5

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

14. Final simplification 3.5

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

Reproduce

herbie shell --seed 2019158 
(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))