Rosa's FloatVsDoubleBenchmark

Average Error: 0.5 → 1.4

Time: 10.4s

Precision: 64

Math

\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;2 \cdot x2 \le -1.0334832093066934 \cdot 10^{161}:\\ \;\;\;\;\left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \log \left(e^{\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(x1 \cdot x1\right)}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\\ \mathbf{elif}\;2 \cdot x2 \le 4.3177529777120672 \cdot 10^{72}:\\ \;\;\;\;\left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \frac{\left(\left(\left(2 \cdot x1\right) \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right)\right) \cdot \sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)} \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) - 6 \cdot 6\right)}\right) \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}\right)}{\left(x1 \cdot x1 + 1\right) \cdot \sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6}} \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(\left(x1 \cdot x1\right) \cdot \sqrt{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6}\right) \cdot \sqrt{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\\ \end{array}\]

C

double code(double x1, double x2) {
	return ((double) (x1 + ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (2.0 * x1)) * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) * ((double) (((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))) - 3.0)))) + ((double) (((double) (x1 * x1)) * ((double) (((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) - 6.0)))))) * ((double) (((double) (x1 * x1)) + 1.0)))) + ((double) (((double) (((double) (3.0 * x1)) * x1)) * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))))) + ((double) (((double) (x1 * x1)) * x1)))) + x1)) + ((double) (3.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) - ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0))))))))));
}

↓

double code(double x1, double x2) {
	double VAR;
	if ((((double) (2.0 * x2)) <= -1.0334832093066934e+161)) {
		VAR = ((double) (((double) (((double) (x1 + ((double) (3.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) - ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))))) + ((double) (x1 + ((double) (((double) (((double) (((double) (((double) (((double) (2.0 * x1)) * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) * ((double) (((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))) - 3.0)))) + ((double) log(((double) exp(((double) (((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) * ((double) (x1 * x1)))))))))) + ((double) (((double) (x1 * x1)) * ((double) -(6.0)))))) * ((double) (((double) (x1 * x1)) + 1.0)))))))) + ((double) (((double) (x1 * x1)) * ((double) (x1 + ((double) (((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))) * 3.0))))))));
	} else {
		double VAR_1;
		if ((((double) (2.0 * x2)) <= 4.317752977712067e+72)) {
			VAR_1 = ((double) (((double) (((double) (x1 + ((double) (3.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) - ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))))) + ((double) (x1 + ((double) (((double) (((double) (((double) (((double) (((double) (((double) (2.0 * x1)) * ((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)))) * ((double) (((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))) - 3.0)))) * ((double) cbrt(((double) (((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) + 6.0)))))) + ((double) (((double) (((double) (x1 * x1)) + 1.0)) * ((double) (((double) (((double) cbrt(((double) (((double) (x1 * x1)) * ((double) (((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) - 6.0)))))) * ((double) cbrt(((double) (((double) (x1 * x1)) * ((double) (((double) (((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) * ((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))))) - ((double) (6.0 * 6.0)))))))))) * ((double) cbrt(((double) (((double) (x1 * x1)) * ((double) (((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) - 6.0)))))))))))) / ((double) (((double) (((double) (x1 * x1)) + 1.0)) * ((double) cbrt(((double) (((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) + 6.0)))))))) * ((double) (((double) (x1 * x1)) + 1.0)))))))) + ((double) (((double) (x1 * x1)) * ((double) (x1 + ((double) (((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))) * 3.0))))))));
		} else {
			VAR_1 = ((double) (((double) (((double) (x1 + ((double) (3.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) - ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))))) + ((double) (x1 + ((double) (((double) (((double) (((double) (((double) (2.0 * x1)) * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) * ((double) (((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))) - 3.0)))) + ((double) (((double) (((double) (x1 * x1)) * ((double) sqrt(((double) (((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) - 6.0)))))) * ((double) sqrt(((double) (((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) - 6.0)))))))) * ((double) (((double) (x1 * x1)) + 1.0)))))))) + ((double) (((double) (x1 * x1)) * ((double) (x1 + ((double) (((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))) * 3.0))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x1

Bits error versus x2

Derivation

1. Split input into 3 regimes

2. if (* 2.0 x2) < -1.0334832093066934e+161

   1. Initial program 0.2

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

   2. Simplified 0.2

      \[\leadsto \color{blue}{\left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)}\]
   3. Using strategy rm

   4. Applied sub-neg 0.2

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \color{blue}{\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(-6\right)\right)}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   5. Applied distribute-lft-in 0.2

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right)}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   6. Applied associate-+r+ 0.2

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \color{blue}{\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right)} \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   7. Simplified 0.2

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\color{blue}{\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(x1 \cdot x1\right)\right)} + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]
   8. Using strategy rm

   9. Applied add-log-exp 6.1

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{\log \left(e^{\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(x1 \cdot x1\right)}\right)}\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   if -1.0334832093066934e+161 < (* 2.0 x2) < 4.317752977712067e+72

   1. Initial program 0.6

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

   2. Simplified 0.6

      \[\leadsto \color{blue}{\left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)}\]
   3. Using strategy rm

   4. Applied add-cube-cbrt 0.7

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{\left(\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)} \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}\right) \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]
   5. Using strategy rm

   6. Applied flip-- 1.1

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)} \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}\right) \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \color{blue}{\frac{\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) - 6 \cdot 6}{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6}}}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   7. Applied associate-*r/ 1.1

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)} \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}\right) \cdot \sqrt[3]{\color{blue}{\frac{\left(x1 \cdot x1\right) \cdot \left(\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) - 6 \cdot 6\right)}{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6}}}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   8. Applied cbrt-div 1.1

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)} \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}\right) \cdot \color{blue}{\frac{\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) - 6 \cdot 6\right)}}{\sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6}}}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   9. Applied associate-*r/ 1.1

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{\frac{\left(\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)} \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}\right) \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) - 6 \cdot 6\right)}}{\sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6}}}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   10. Applied associate-*r/ 1.1

       \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\color{blue}{\frac{\left(2 \cdot x1\right) \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right)}{x1 \cdot x1 + 1}} \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \frac{\left(\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)} \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}\right) \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) - 6 \cdot 6\right)}}{\sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6}}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   11. Applied associate-*l/ 1.1

       \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\color{blue}{\frac{\left(\left(2 \cdot x1\right) \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right)}{x1 \cdot x1 + 1}} + \frac{\left(\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)} \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}\right) \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) - 6 \cdot 6\right)}}{\sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6}}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   12. Applied frac-add 1.2

       \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \color{blue}{\frac{\left(\left(\left(2 \cdot x1\right) \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right)\right) \cdot \sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)} \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}\right) \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) - 6 \cdot 6\right)}\right)}{\left(x1 \cdot x1 + 1\right) \cdot \sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6}}} \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   13. Simplified 1.2

       \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \frac{\color{blue}{\left(\left(\left(2 \cdot x1\right) \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right)\right) \cdot \sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)} \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) - 6 \cdot 6\right)}\right) \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}\right)}}{\left(x1 \cdot x1 + 1\right) \cdot \sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6}} \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   if 4.317752977712067e+72 < (* 2.0 x2)

   1. Initial program 0.3

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

   2. Simplified 0.3

      \[\leadsto \color{blue}{\left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)}\]
   3. Using strategy rm

   4. Applied add-sqr-sqrt 0.3

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \color{blue}{\left(\sqrt{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6} \cdot \sqrt{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6}\right)}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]

   5. Applied associate-*r* 0.3

      \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \sqrt{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6}\right) \cdot \sqrt{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6}}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\]
3. Recombined 3 regimes into one program.

4. Final simplification 1.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x2 \le -1.0334832093066934 \cdot 10^{161}:\\ \;\;\;\;\left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \log \left(e^{\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(x1 \cdot x1\right)}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\\ \mathbf{elif}\;2 \cdot x2 \le 4.3177529777120672 \cdot 10^{72}:\\ \;\;\;\;\left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \frac{\left(\left(\left(2 \cdot x1\right) \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right)\right) \cdot \sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)} \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) - 6 \cdot 6\right)}\right) \cdot \sqrt[3]{\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)}\right)}{\left(x1 \cdot x1 + 1\right) \cdot \sqrt[3]{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + 6}} \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(\left(x1 \cdot x1\right) \cdot \sqrt{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6}\right) \cdot \sqrt{4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6}\right) \cdot \left(x1 \cdot x1 + 1\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(x1 + \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 3\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020123 
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  :precision binary64
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6))) (+ (* x1 x1) 1)) (* (* (* 3 x1) x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (* (* x1 x1) x1)) x1) (* 3 (/ (- (- (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))))))