(- (/ x0 (- 1 x1)) x0)

Average Error: 8.3 → 4.3

Time: 5.6s

Precision: 64

\[x0 = 1.855 \land x1 = 2.09000000000000012 \cdot 10^{-4} \lor x0 = 2.98499999999999988 \land x1 = 0.018599999999999998\]

Math

\[\frac{x0}{1 - x1} - x0\]

↓

\[\begin{array}{l} \mathbf{if}\;1 - x1 \le 0.99059549999999996:\\ \;\;\;\;\frac{\frac{\left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} + {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right) \cdot \left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right)}{\left(\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) + {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\left({\left(\sqrt{\frac{\sqrt{x0}}{\sqrt[3]{1 - x1} \cdot \sqrt[3]{1 - x1}}}\right)}^{6} \cdot {\left(\sqrt{\frac{\sqrt{x0}}{\sqrt[3]{1 - x1}}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) - {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)}}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} - {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\frac{x0}{1 - x1} + \left(-x0\right)\right)}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\sqrt{\frac{x0}{1 - x1}} - \sqrt{x0}\right)}\\ \end{array}\]

C

double code(double x0, double x1) {
	return ((x0 / (1.0 - x1)) - x0);
}

↓

double code(double x0, double x1) {
	double temp;
	if (((1.0 - x1) <= 0.9905955)) {
		temp = ((((pow(pow(sqrt((x0 / (1.0 - x1))), 3.0), 3.0) + pow(pow(sqrt(x0), 3.0), 3.0)) * (pow(pow(sqrt((x0 / (1.0 - x1))), 3.0), 3.0) - pow(pow(sqrt(x0), 3.0), 3.0))) / (((pow(sqrt((x0 / (1.0 - x1))), 6.0) + pow(sqrt(x0), 6.0)) + (pow(sqrt((x0 / (1.0 - x1))), 3.0) * pow(sqrt(x0), 3.0))) * (((pow(sqrt((sqrt(x0) / (cbrt((1.0 - x1)) * cbrt((1.0 - x1))))), 6.0) * pow(sqrt((sqrt(x0) / cbrt((1.0 - x1)))), 6.0)) + pow(sqrt(x0), 6.0)) - (pow(sqrt((x0 / (1.0 - x1))), 3.0) * pow(sqrt(x0), 3.0))))) / ((((x0 / (1.0 - x1)) + x0) + (sqrt((x0 / (1.0 - x1))) * sqrt(x0))) * (((x0 / (1.0 - x1)) + x0) - (sqrt((x0 / (1.0 - x1))) * sqrt(x0)))));
	} else {
		temp = (((pow(sqrt((x0 / (1.0 - x1))), 3.0) - pow(sqrt(x0), 3.0)) * ((x0 / (1.0 - x1)) + -x0)) / ((((x0 / (1.0 - x1)) + x0) + (sqrt((x0 / (1.0 - x1))) * sqrt(x0))) * (sqrt((x0 / (1.0 - x1))) - sqrt(x0))));
	}
	return temp;
}

Error

Bits error versus x0

Bits error versus x1

Target

Original	8.3
Target	0.5
Herbie	4.3

\[\frac{x0 \cdot x1}{1 - x1}\]

Derivation

1. Split input into 2 regimes

2. if (- 1.0 x1) < 0.9905955

   1. Initial program 5.5

      \[\frac{x0}{1 - x1} - x0\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt 5.5

      \[\leadsto \frac{x0}{1 - x1} - \color{blue}{\sqrt{x0} \cdot \sqrt{x0}}\]

   4. Applied add-sqr-sqrt 4.4

      \[\leadsto \color{blue}{\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}}} - \sqrt{x0} \cdot \sqrt{x0}\]

   5. Applied difference-of-squares 4.6

      \[\leadsto \color{blue}{\left(\sqrt{\frac{x0}{1 - x1}} + \sqrt{x0}\right) \cdot \left(\sqrt{\frac{x0}{1 - x1}} - \sqrt{x0}\right)}\]
   6. Using strategy rm

   7. Applied flip3-- 3.5

      \[\leadsto \left(\sqrt{\frac{x0}{1 - x1}} + \sqrt{x0}\right) \cdot \color{blue}{\frac{{\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} - {\left(\sqrt{x0}\right)}^{3}}{\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}} + \left(\sqrt{x0} \cdot \sqrt{x0} + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}}\]

   8. Applied flip3-+ 3.6

      \[\leadsto \color{blue}{\frac{{\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} + {\left(\sqrt{x0}\right)}^{3}}{\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}} + \left(\sqrt{x0} \cdot \sqrt{x0} - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}} \cdot \frac{{\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} - {\left(\sqrt{x0}\right)}^{3}}{\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}} + \left(\sqrt{x0} \cdot \sqrt{x0} + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\]

   9. Applied frac-times 3.6

      \[\leadsto \color{blue}{\frac{\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} + {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} - {\left(\sqrt{x0}\right)}^{3}\right)}{\left(\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}} + \left(\sqrt{x0} \cdot \sqrt{x0} - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)\right) \cdot \left(\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}} + \left(\sqrt{x0} \cdot \sqrt{x0} + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)\right)}}\]

   10. Simplified 3.2

       \[\leadsto \frac{\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} + {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} - {\left(\sqrt{x0}\right)}^{3}\right)}{\color{blue}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}}\]
   11. Using strategy rm

   12. Applied flip3-- 2.6

       \[\leadsto \frac{\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} + {\left(\sqrt{x0}\right)}^{3}\right) \cdot \color{blue}{\frac{{\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}}{{\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} + \left({\left(\sqrt{x0}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3} + {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)}}}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\]

   13. Applied flip3-+ 2.6

       \[\leadsto \frac{\color{blue}{\frac{{\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} + {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}}{{\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} + \left({\left(\sqrt{x0}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3} - {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)}} \cdot \frac{{\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}}{{\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} + \left({\left(\sqrt{x0}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3} + {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)}}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\]

   14. Applied frac-times 2.6

       \[\leadsto \frac{\color{blue}{\frac{\left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} + {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right) \cdot \left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right)}{\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} + \left({\left(\sqrt{x0}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3} - {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)\right) \cdot \left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} + \left({\left(\sqrt{x0}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3} + {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)\right)}}}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\]

   15. Simplified 2.6

       \[\leadsto \frac{\frac{\left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} + {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right) \cdot \left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right)}{\color{blue}{\left(\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) + {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) - {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)}}}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\]
   16. Using strategy rm

   17. Applied add-cube-cbrt 0

       \[\leadsto \frac{\frac{\left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} + {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right) \cdot \left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right)}{\left(\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) + {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\left({\left(\sqrt{\frac{x0}{\color{blue}{\left(\sqrt[3]{1 - x1} \cdot \sqrt[3]{1 - x1}\right) \cdot \sqrt[3]{1 - x1}}}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) - {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)}}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\]

   18. Applied add-sqr-sqrt 0

       \[\leadsto \frac{\frac{\left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} + {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right) \cdot \left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right)}{\left(\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) + {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\left({\left(\sqrt{\frac{\color{blue}{\sqrt{x0} \cdot \sqrt{x0}}}{\left(\sqrt[3]{1 - x1} \cdot \sqrt[3]{1 - x1}\right) \cdot \sqrt[3]{1 - x1}}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) - {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)}}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\]

   19. Applied times-frac 0

       \[\leadsto \frac{\frac{\left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} + {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right) \cdot \left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right)}{\left(\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) + {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\left({\left(\sqrt{\color{blue}{\frac{\sqrt{x0}}{\sqrt[3]{1 - x1} \cdot \sqrt[3]{1 - x1}} \cdot \frac{\sqrt{x0}}{\sqrt[3]{1 - x1}}}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) - {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)}}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\]

   20. Applied sqrt-prod 0

       \[\leadsto \frac{\frac{\left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} + {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right) \cdot \left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right)}{\left(\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) + {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\left({\color{blue}{\left(\sqrt{\frac{\sqrt{x0}}{\sqrt[3]{1 - x1} \cdot \sqrt[3]{1 - x1}}} \cdot \sqrt{\frac{\sqrt{x0}}{\sqrt[3]{1 - x1}}}\right)}}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) - {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)}}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\]

   21. Applied unpow-prod-down 0

       \[\leadsto \frac{\frac{\left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} + {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right) \cdot \left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right)}{\left(\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) + {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\left(\color{blue}{{\left(\sqrt{\frac{\sqrt{x0}}{\sqrt[3]{1 - x1} \cdot \sqrt[3]{1 - x1}}}\right)}^{6} \cdot {\left(\sqrt{\frac{\sqrt{x0}}{\sqrt[3]{1 - x1}}}\right)}^{6}} + {\left(\sqrt{x0}\right)}^{6}\right) - {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)}}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\]

   if 0.9905955 < (- 1.0 x1)

   1. Initial program 11.3

      \[\frac{x0}{1 - x1} - x0\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt 11.3

      \[\leadsto \frac{x0}{1 - x1} - \color{blue}{\sqrt{x0} \cdot \sqrt{x0}}\]

   4. Applied add-sqr-sqrt 10.7

      \[\leadsto \color{blue}{\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}}} - \sqrt{x0} \cdot \sqrt{x0}\]

   5. Applied difference-of-squares 10.7

      \[\leadsto \color{blue}{\left(\sqrt{\frac{x0}{1 - x1}} + \sqrt{x0}\right) \cdot \left(\sqrt{\frac{x0}{1 - x1}} - \sqrt{x0}\right)}\]
   6. Using strategy rm

   7. Applied flip3-- 12.1

      \[\leadsto \left(\sqrt{\frac{x0}{1 - x1}} + \sqrt{x0}\right) \cdot \color{blue}{\frac{{\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} - {\left(\sqrt{x0}\right)}^{3}}{\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}} + \left(\sqrt{x0} \cdot \sqrt{x0} + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}}\]

   8. Applied flip-+ 12.1

      \[\leadsto \color{blue}{\frac{\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}} - \sqrt{x0} \cdot \sqrt{x0}}{\sqrt{\frac{x0}{1 - x1}} - \sqrt{x0}}} \cdot \frac{{\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} - {\left(\sqrt{x0}\right)}^{3}}{\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}} + \left(\sqrt{x0} \cdot \sqrt{x0} + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\]

   9. Applied frac-times 12.1

      \[\leadsto \color{blue}{\frac{\left(\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}} - \sqrt{x0} \cdot \sqrt{x0}\right) \cdot \left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} - {\left(\sqrt{x0}\right)}^{3}\right)}{\left(\sqrt{\frac{x0}{1 - x1}} - \sqrt{x0}\right) \cdot \left(\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}} + \left(\sqrt{x0} \cdot \sqrt{x0} + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)\right)}}\]

   10. Simplified 8.7

       \[\leadsto \frac{\color{blue}{\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} - {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\frac{x0}{1 - x1} + \left(-x0\right)\right)}}{\left(\sqrt{\frac{x0}{1 - x1}} - \sqrt{x0}\right) \cdot \left(\sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{\frac{x0}{1 - x1}} + \left(\sqrt{x0} \cdot \sqrt{x0} + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)\right)}\]

   11. Simplified 8.7

       \[\leadsto \frac{\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} - {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\frac{x0}{1 - x1} + \left(-x0\right)\right)}{\color{blue}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\sqrt{\frac{x0}{1 - x1}} - \sqrt{x0}\right)}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 4.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - x1 \le 0.99059549999999996:\\ \;\;\;\;\frac{\frac{\left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} + {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right) \cdot \left({\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{x0}\right)}^{3}\right)}^{3}\right)}{\left(\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) + {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\left({\left(\sqrt{\frac{\sqrt{x0}}{\sqrt[3]{1 - x1} \cdot \sqrt[3]{1 - x1}}}\right)}^{6} \cdot {\left(\sqrt{\frac{\sqrt{x0}}{\sqrt[3]{1 - x1}}}\right)}^{6} + {\left(\sqrt{x0}\right)}^{6}\right) - {\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} \cdot {\left(\sqrt{x0}\right)}^{3}\right)}}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\left(\frac{x0}{1 - x1} + x0\right) - \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left({\left(\sqrt{\frac{x0}{1 - x1}}\right)}^{3} - {\left(\sqrt{x0}\right)}^{3}\right) \cdot \left(\frac{x0}{1 - x1} + \left(-x0\right)\right)}{\left(\left(\frac{x0}{1 - x1} + x0\right) + \sqrt{\frac{x0}{1 - x1}} \cdot \sqrt{x0}\right) \cdot \left(\sqrt{\frac{x0}{1 - x1}} - \sqrt{x0}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020066 
(FPCore (x0 x1)
  :name "(- (/ x0 (- 1 x1)) x0)"
  :precision binary64
  :pre (or (and (== x0 1.855) (== x1 0.000209)) (and (== x0 2.985) (== x1 0.0186)))

  :herbie-target
  (/ (* x0 x1) (- 1 x1))

  (- (/ x0 (- 1 x1)) x0))