Jmat.Real.dawson

Average Error: 4.4 → 3.6

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\]

↓

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

C

double f(double x) {
        double r5782701 = 1.0;
        double r5782702 = /* ERROR: no posit support in C */;
        double r5782703 = 0.1049934947;
        double r5782704 = /* ERROR: no posit support in C */;
        double r5782705 = x;
        double r5782706 = r5782705 * r5782705;
        double r5782707 = r5782704 * r5782706;
        double r5782708 = r5782702 + r5782707;
        double r5782709 = 0.0424060604;
        double r5782710 = /* ERROR: no posit support in C */;
        double r5782711 = r5782706 * r5782706;
        double r5782712 = r5782710 * r5782711;
        double r5782713 = r5782708 + r5782712;
        double r5782714 = 0.0072644182;
        double r5782715 = /* ERROR: no posit support in C */;
        double r5782716 = r5782711 * r5782706;
        double r5782717 = r5782715 * r5782716;
        double r5782718 = r5782713 + r5782717;
        double r5782719 = 0.0005064034;
        double r5782720 = /* ERROR: no posit support in C */;
        double r5782721 = r5782716 * r5782706;
        double r5782722 = r5782720 * r5782721;
        double r5782723 = r5782718 + r5782722;
        double r5782724 = 0.0001789971;
        double r5782725 = /* ERROR: no posit support in C */;
        double r5782726 = r5782721 * r5782706;
        double r5782727 = r5782725 * r5782726;
        double r5782728 = r5782723 + r5782727;
        double r5782729 = 0.7715471019;
        double r5782730 = /* ERROR: no posit support in C */;
        double r5782731 = r5782730 * r5782706;
        double r5782732 = r5782702 + r5782731;
        double r5782733 = 0.2909738639;
        double r5782734 = /* ERROR: no posit support in C */;
        double r5782735 = r5782734 * r5782711;
        double r5782736 = r5782732 + r5782735;
        double r5782737 = 0.0694555761;
        double r5782738 = /* ERROR: no posit support in C */;
        double r5782739 = r5782738 * r5782716;
        double r5782740 = r5782736 + r5782739;
        double r5782741 = 0.0140005442;
        double r5782742 = /* ERROR: no posit support in C */;
        double r5782743 = r5782742 * r5782721;
        double r5782744 = r5782740 + r5782743;
        double r5782745 = 0.0008327945;
        double r5782746 = /* ERROR: no posit support in C */;
        double r5782747 = r5782746 * r5782726;
        double r5782748 = r5782744 + r5782747;
        double r5782749 = 2.0;
        double r5782750 = /* ERROR: no posit support in C */;
        double r5782751 = r5782750 * r5782725;
        double r5782752 = r5782726 * r5782706;
        double r5782753 = r5782751 * r5782752;
        double r5782754 = r5782748 + r5782753;
        double r5782755 = r5782728 / r5782754;
        double r5782756 = r5782755 * r5782705;
        return r5782756;
}

↓

double f(double x) {
        double r5782757 = 1.0;
        double r5782758 = /* ERROR: no posit support in C */;
        double r5782759 = 1.0;
        double r5782760 = /* ERROR: no posit support in C */;
        double r5782761 = x;
        double r5782762 = r5782761 * r5782761;
        double r5782763 = 0.7715471019;
        double r5782764 = /* ERROR: no posit support in C */;
        double r5782765 = 0.2909738639;
        double r5782766 = /* ERROR: no posit support in C */;
        double r5782767 = r5782766 * r5782762;
        double r5782768 = r5782764 + r5782767;
        double r5782769 = r5782762 * r5782762;
        double r5782770 = 0.0694555761;
        double r5782771 = /* ERROR: no posit support in C */;
        double r5782772 = 0.0001789971;
        double r5782773 = /* ERROR: no posit support in C */;
        double r5782774 = r5782773 * r5782762;
        double r5782775 = 2.0;
        double r5782776 = /* ERROR: no posit support in C */;
        double r5782777 = r5782774 * r5782776;
        double r5782778 = 0.0008327945;
        double r5782779 = /* ERROR: no posit support in C */;
        double r5782780 = r5782777 + r5782779;
        double r5782781 = r5782780 * r5782769;
        double r5782782 = r5782771 + r5782781;
        double r5782783 = r5782769 * r5782782;
        double r5782784 = r5782768 + r5782783;
        double r5782785 = r5782762 * r5782784;
        double r5782786 = r5782760 + r5782785;
        double r5782787 = 0.0140005442;
        double r5782788 = /* ERROR: no posit support in C */;
        double r5782789 = r5782788 * r5782769;
        double r5782790 = r5782789 * r5782769;
        double r5782791 = r5782786 + r5782790;
        double r5782792 = 0.1049934947;
        double r5782793 = /* ERROR: no posit support in C */;
        double r5782794 = 0.0005064034;
        double r5782795 = /* ERROR: no posit support in C */;
        double r5782796 = r5782795 + r5782774;
        double r5782797 = r5782762 * r5782796;
        double r5782798 = 0.0072644182;
        double r5782799 = /* ERROR: no posit support in C */;
        double r5782800 = r5782797 + r5782799;
        double r5782801 = r5782762 * r5782800;
        double r5782802 = 0.0424060604;
        double r5782803 = /* ERROR: no posit support in C */;
        double r5782804 = r5782801 + r5782803;
        double r5782805 = r5782762 * r5782804;
        double r5782806 = r5782793 + r5782805;
        double r5782807 = r5782762 * r5782806;
        double r5782808 = r5782807 + r5782760;
        double r5782809 = r5782791 / r5782808;
        double r5782810 = r5782758 / r5782809;
        double r5782811 = r5782810 * r5782761;
        return r5782811;
}

Error

Bits error versus x

Derivation

1. Initial program 4.4

   \[\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 3.7

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

4. Applied *p16-rgt-identity-expand 3.7

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

5. Applied associate-/l* 3.7

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

6. Simplified 3.6

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

8. Applied p16-*-un-lft-identity 3.6

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

9. Applied associate-/l* 3.6

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

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

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

12. Applied associate-/l* 3.6

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

13. Simplified 3.6

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

14. Final simplification 3.6

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

Reproduce

herbie shell --seed 2019168 
(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))