Average Error: 29.2 → 0.0
Time: 9.3s
Precision: binary64
\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -14780315067.359564 \lor \neg \left(x \leq 567.1332058863363\right):\\ \;\;\;\;\frac{0.2514179000665375}{{x}^{3}} + \left(\frac{0.15298196345929327}{{x}^{5}} + \frac{0.5}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}} \cdot \left(x \cdot \sqrt[3]{\sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}}\right)\\ \end{array}\]
\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \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) + 0.0001789971 \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)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \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) + 0.0008327945 \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) + \left(2 \cdot 0.0001789971\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)} \cdot x
↓
\begin{array}{l}
\mathbf{if}\;x \leq -14780315067.359564 \lor \neg \left(x \leq 567.1332058863363\right):\\
\;\;\;\;\frac{0.2514179000665375}{{x}^{3}} + \left(\frac{0.15298196345929327}{{x}^{5}} + \frac{0.5}{x}\right)\\

\mathbf{else}:\\
\;\;\;\;\sqrt[3]{\sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}} \cdot \left(x \cdot \sqrt[3]{\sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}}\right)\\

\end{array}
(FPCore (x)
 :precision binary64
 (*
  (/
   (+
    (+
     (+
      (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x))))
      (* 0.0072644182 (* (* (* x x) (* x x)) (* x x))))
     (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x))))
    (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x))))
   (+
    (+
     (+
      (+
       (+
        (+ 1.0 (* 0.7715471019 (* x x)))
        (* 0.2909738639 (* (* x x) (* x x))))
       (* 0.0694555761 (* (* (* x x) (* x x)) (* x x))))
      (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x))))
     (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x))))
    (*
     (* 2.0 0.0001789971)
     (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))))
  x))
↓
(FPCore (x)
 :precision binary64
 (if (or (<= x -14780315067.359564) (not (<= x 567.1332058863363)))
   (+
    (/ 0.2514179000665375 (pow x 3.0))
    (+ (/ 0.15298196345929327 (pow x 5.0)) (/ 0.5 x)))
   (*
    (cbrt
     (sqrt
      (pow
       (/
        (+
         1.0
         (+
          (* 0.1049934947 (* x x))
          (+
           (* 0.0424060604 (pow x 4.0))
           (+
            (* 0.0072644182 (pow x 6.0))
            (+ (* 0.0005064034 (pow x 8.0)) (* 0.0001789971 (pow x 10.0)))))))
        (+
         1.0
         (+
          (* x (* x 0.7715471019))
          (+
           (* (pow x 4.0) 0.2909738639)
           (+
            (* (pow x 6.0) 0.0694555761)
            (+
             (* (pow x 8.0) 0.0140005442)
             (+
              (* (pow x 10.0) 0.0008327945)
              (* 0.0001789971 (* 2.0 (pow x 12.0))))))))))
       3.0)))
    (*
     x
     (cbrt
      (sqrt
       (pow
        (/
         (+
          1.0
          (+
           (* 0.1049934947 (* x x))
           (+
            (* 0.0424060604 (pow x 4.0))
            (+
             (* 0.0072644182 (pow x 6.0))
             (+ (* 0.0005064034 (pow x 8.0)) (* 0.0001789971 (pow x 10.0)))))))
         (+
          1.0
          (+
           (* x (* x 0.7715471019))
           (+
            (* (pow x 4.0) 0.2909738639)
            (+
             (* (pow x 6.0) 0.0694555761)
             (+
              (* (pow x 8.0) 0.0140005442)
              (+
               (* (pow x 10.0) 0.0008327945)
               (* 0.0001789971 (* 2.0 (pow x 12.0))))))))))
        3.0)))))))
double code(double x) {
	return ((double) ((((double) (((double) (((double) (((double) (((double) (1.0 + ((double) (0.1049934947 * ((double) (x * x)))))) + ((double) (0.0424060604 * ((double) (((double) (x * x)) * ((double) (x * x)))))))) + ((double) (0.0072644182 * ((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))))))) + ((double) (0.0005064034 * ((double) (((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))))))) + ((double) (0.0001789971 * ((double) (((double) (((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))))))) / ((double) (((double) (((double) (((double) (((double) (((double) (1.0 + ((double) (0.7715471019 * ((double) (x * x)))))) + ((double) (0.2909738639 * ((double) (((double) (x * x)) * ((double) (x * x)))))))) + ((double) (0.0694555761 * ((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))))))) + ((double) (0.0140005442 * ((double) (((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))))))) + ((double) (0.0008327945 * ((double) (((double) (((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))))))) + ((double) (((double) (2.0 * 0.0001789971)) * ((double) (((double) (((double) (((double) (((double) (((double) (x * x)) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x)))) * ((double) (x * x))))))))) * x));
}
↓
double code(double x) {
	double tmp;
	if (((x <= -14780315067.359564) || !(x <= 567.1332058863363))) {
		tmp = ((double) ((0.2514179000665375 / ((double) pow(x, 3.0))) + ((double) ((0.15298196345929327 / ((double) pow(x, 5.0))) + (0.5 / x)))));
	} else {
		tmp = ((double) (((double) cbrt(((double) sqrt(((double) pow((((double) (1.0 + ((double) (((double) (0.1049934947 * ((double) (x * x)))) + ((double) (((double) (0.0424060604 * ((double) pow(x, 4.0)))) + ((double) (((double) (0.0072644182 * ((double) pow(x, 6.0)))) + ((double) (((double) (0.0005064034 * ((double) pow(x, 8.0)))) + ((double) (0.0001789971 * ((double) pow(x, 10.0)))))))))))))) / ((double) (1.0 + ((double) (((double) (x * ((double) (x * 0.7715471019)))) + ((double) (((double) (((double) pow(x, 4.0)) * 0.2909738639)) + ((double) (((double) (((double) pow(x, 6.0)) * 0.0694555761)) + ((double) (((double) (((double) pow(x, 8.0)) * 0.0140005442)) + ((double) (((double) (((double) pow(x, 10.0)) * 0.0008327945)) + ((double) (0.0001789971 * ((double) (2.0 * ((double) pow(x, 12.0))))))))))))))))))), 3.0)))))) * ((double) (x * ((double) cbrt(((double) sqrt(((double) pow((((double) (1.0 + ((double) (((double) (0.1049934947 * ((double) (x * x)))) + ((double) (((double) (0.0424060604 * ((double) pow(x, 4.0)))) + ((double) (((double) (0.0072644182 * ((double) pow(x, 6.0)))) + ((double) (((double) (0.0005064034 * ((double) pow(x, 8.0)))) + ((double) (0.0001789971 * ((double) pow(x, 10.0)))))))))))))) / ((double) (1.0 + ((double) (((double) (x * ((double) (x * 0.7715471019)))) + ((double) (((double) (((double) pow(x, 4.0)) * 0.2909738639)) + ((double) (((double) (((double) pow(x, 6.0)) * 0.0694555761)) + ((double) (((double) (((double) pow(x, 8.0)) * 0.0140005442)) + ((double) (((double) (((double) pow(x, 10.0)) * 0.0008327945)) + ((double) (0.0001789971 * ((double) (2.0 * ((double) pow(x, 12.0))))))))))))))))))), 3.0))))))))));
	}
	return tmp;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if x < -14780315067.3595638 or 567.13320588633633 < x

    1. Initial program Error: 59.8 bits

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

    2. SimplifiedError: 59.8 bits

      \[\leadsto \color{blue}{x \cdot \frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(\left(x \cdot \left(x \cdot 0.7715471019\right) + {x}^{4} \cdot 0.2909738639\right) + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)}}\]

    3. Taylor expanded around inf Error: 0.0 bits

      \[\leadsto \color{blue}{0.2514179000665375 \cdot \frac{1}{{x}^{3}} + \left(0.15298196345929327 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)}\]

    4. SimplifiedError: 0.0 bits

      \[\leadsto \color{blue}{\frac{0.2514179000665375}{{x}^{3}} + \left(\frac{0.15298196345929327}{{x}^{5}} + \frac{0.5}{x}\right)}\]

    if -14780315067.3595638 < x < 567.13320588633633

    1. Initial program Error: 0.0 bits

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

    2. SimplifiedError: 0.0 bits

      \[\leadsto \color{blue}{x \cdot \frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(\left(x \cdot \left(x \cdot 0.7715471019\right) + {x}^{4} \cdot 0.2909738639\right) + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)}}\]
    3. Using strategy rm

    4. Applied add-cbrt-cubeError: 0.2 bits

      \[\leadsto x \cdot \frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{\color{blue}{\sqrt[3]{\left(\left(1 + \left(\left(x \cdot \left(x \cdot 0.7715471019\right) + {x}^{4} \cdot 0.2909738639\right) + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right) \cdot \left(1 + \left(\left(x \cdot \left(x \cdot 0.7715471019\right) + {x}^{4} \cdot 0.2909738639\right) + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)\right) \cdot \left(1 + \left(\left(x \cdot \left(x \cdot 0.7715471019\right) + {x}^{4} \cdot 0.2909738639\right) + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}}}\]

    5. Applied add-cbrt-cubeError: 0.2 bits

      \[\leadsto x \cdot \frac{\color{blue}{\sqrt[3]{\left(\left(1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)\right) \cdot \left(1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)\right)\right) \cdot \left(1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)\right)}}}{\sqrt[3]{\left(\left(1 + \left(\left(x \cdot \left(x \cdot 0.7715471019\right) + {x}^{4} \cdot 0.2909738639\right) + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right) \cdot \left(1 + \left(\left(x \cdot \left(x \cdot 0.7715471019\right) + {x}^{4} \cdot 0.2909738639\right) + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)\right) \cdot \left(1 + \left(\left(x \cdot \left(x \cdot 0.7715471019\right) + {x}^{4} \cdot 0.2909738639\right) + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}}\]

    6. Applied cbrt-undivError: 0.2 bits

      \[\leadsto x \cdot \color{blue}{\sqrt[3]{\frac{\left(\left(1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)\right) \cdot \left(1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)\right)\right) \cdot \left(1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)\right)}{\left(\left(1 + \left(\left(x \cdot \left(x \cdot 0.7715471019\right) + {x}^{4} \cdot 0.2909738639\right) + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right) \cdot \left(1 + \left(\left(x \cdot \left(x \cdot 0.7715471019\right) + {x}^{4} \cdot 0.2909738639\right) + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)\right) \cdot \left(1 + \left(\left(x \cdot \left(x \cdot 0.7715471019\right) + {x}^{4} \cdot 0.2909738639\right) + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}}}\]

    7. SimplifiedError: 0.0 bits

      \[\leadsto x \cdot \sqrt[3]{\color{blue}{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}}\]
    8. Using strategy rm

    9. Applied add-sqr-sqrtError: 0.0 bits

      \[\leadsto x \cdot \sqrt[3]{\color{blue}{\sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}} \cdot \sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}}}\]

    10. Applied cbrt-prodError: 0.1 bits

      \[\leadsto x \cdot \color{blue}{\left(\sqrt[3]{\sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}} \cdot \sqrt[3]{\sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}}\right)}\]

    11. Applied associate-*r*Error: 0.1 bits

      \[\leadsto \color{blue}{\left(x \cdot \sqrt[3]{\sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}}\right) \cdot \sqrt[3]{\sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplificationError: 0.0 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -14780315067.359564 \lor \neg \left(x \leq 567.1332058863363\right):\\ \;\;\;\;\frac{0.2514179000665375}{{x}^{3}} + \left(\frac{0.15298196345929327}{{x}^{5}} + \frac{0.5}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}} \cdot \left(x \cdot \sqrt[3]{\sqrt{{\left(\frac{1 + \left(0.1049934947 \cdot \left(x \cdot x\right) + \left(0.0424060604 \cdot {x}^{4} + \left(0.0072644182 \cdot {x}^{6} + \left(0.0005064034 \cdot {x}^{8} + 0.0001789971 \cdot {x}^{10}\right)\right)\right)\right)}{1 + \left(x \cdot \left(x \cdot 0.7715471019\right) + \left({x}^{4} \cdot 0.2909738639 + \left({x}^{6} \cdot 0.0694555761 + \left({x}^{8} \cdot 0.0140005442 + \left({x}^{10} \cdot 0.0008327945 + 0.0001789971 \cdot \left(2 \cdot {x}^{12}\right)\right)\right)\right)\right)\right)}\right)}^{3}}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(FPCore (x)
  :name "Jmat.Real.dawson"
  :precision binary64
  (* (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x))