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

Average Error: 7.8 → 3.9

Time: 4.3s

Precision: 64

• could not determine a ground truth for program pre

  1. x0 = 1.855
  2. x1 = 0.0186

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x1 \le 2.12089080810546861 \cdot 10^{-4}:\\ \;\;\;\;\frac{\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{6} + \left(-{\left(x0 \cdot x0\right)}^{6}\right)}{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} + {\left(x0 \cdot x0\right)}^{3}}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} - {\left({\left(x0 \cdot x0\right)}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \end{array}\]

C

double f(double x0, double x1) {
        double r205631 = x0;
        double r205632 = 1.0;
        double r205633 = x1;
        double r205634 = r205632 - r205633;
        double r205635 = r205631 / r205634;
        double r205636 = r205635 - r205631;
        return r205636;
}

↓

double f(double x0, double x1) {
        double r205637 = x1;
        double r205638 = 0.00021208908081054686;
        bool r205639 = r205637 <= r205638;
        double r205640 = x0;
        double r205641 = cbrt(r205640);
        double r205642 = r205641 * r205641;
        double r205643 = 1.0;
        double r205644 = r205643 - r205637;
        double r205645 = sqrt(r205644);
        double r205646 = r205642 / r205645;
        double r205647 = r205641 / r205645;
        double r205648 = r205646 * r205647;
        double r205649 = r205640 / r205644;
        double r205650 = r205648 * r205649;
        double r205651 = 6.0;
        double r205652 = pow(r205650, r205651);
        double r205653 = r205640 * r205640;
        double r205654 = pow(r205653, r205651);
        double r205655 = -r205654;
        double r205656 = r205652 + r205655;
        double r205657 = 3.0;
        double r205658 = pow(r205650, r205657);
        double r205659 = pow(r205653, r205657);
        double r205660 = r205658 + r205659;
        double r205661 = r205656 / r205660;
        double r205662 = 2.0;
        double r205663 = pow(r205640, r205662);
        double r205664 = r205663 + r205650;
        double r205665 = r205663 * r205664;
        double r205666 = r205650 * r205650;
        double r205667 = r205665 + r205666;
        double r205668 = r205661 / r205667;
        double r205669 = r205649 + r205640;
        double r205670 = r205668 / r205669;
        double r205671 = sqrt(r205657);
        double r205672 = pow(r205653, r205671);
        double r205673 = pow(r205672, r205671);
        double r205674 = r205658 - r205673;
        double r205675 = r205674 / r205667;
        double r205676 = r205675 / r205669;
        double r205677 = r205639 ? r205670 : r205676;
        return r205677;
}

Error

Bits error versus x0

Bits error versus x1

Target

Original	7.8
Target	0.3
Herbie	3.9

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

Derivation

1. Split input into 2 regimes

2. if x1 < 0.00021208908081054686

   1. Initial program 11.2

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

   3. Applied flip-- 11.4

      \[\leadsto \color{blue}{\frac{\frac{x0}{1 - x1} \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}}\]
   4. Using strategy rm

   5. Applied add-sqr-sqrt 8.1

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

   6. Applied add-cube-cbrt 8.1

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

   7. Applied times-frac 8.1

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

   9. Applied flip3-- 8.0

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

   10. Simplified 8.0

       \[\leadsto \frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} - {\left(x0 \cdot x0\right)}^{3}}{\color{blue}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}}{\frac{x0}{1 - x1} + x0}\]
   11. Using strategy rm

   12. Applied flip-- 7.6

       \[\leadsto \frac{\frac{\color{blue}{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} \cdot {\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} - {\left(x0 \cdot x0\right)}^{3} \cdot {\left(x0 \cdot x0\right)}^{3}}{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} + {\left(x0 \cdot x0\right)}^{3}}}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\]

   13. Simplified 7.3

       \[\leadsto \frac{\frac{\frac{\color{blue}{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{6} + \left(-{\left(x0 \cdot x0\right)}^{6}\right)}}{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} + {\left(x0 \cdot x0\right)}^{3}}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\]

   if 0.00021208908081054686 < x1

   1. Initial program 4.5

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

   3. Applied flip-- 3.2

      \[\leadsto \color{blue}{\frac{\frac{x0}{1 - x1} \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}}\]
   4. Using strategy rm

   5. Applied add-sqr-sqrt 3.2

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

   6. Applied add-cube-cbrt 3.2

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

   7. Applied times-frac 5.2

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

   9. Applied flip3-- 5.1

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

   10. Simplified 5.2

       \[\leadsto \frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} - {\left(x0 \cdot x0\right)}^{3}}{\color{blue}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}}{\frac{x0}{1 - x1} + x0}\]
   11. Using strategy rm

   12. Applied add-sqr-sqrt 2.2

       \[\leadsto \frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} - {\left(x0 \cdot x0\right)}^{\color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)}}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\]

   13. Applied pow-unpow 0.5

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

4. Final simplification 3.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \le 2.12089080810546861 \cdot 10^{-4}:\\ \;\;\;\;\frac{\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{6} + \left(-{\left(x0 \cdot x0\right)}^{6}\right)}{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} + {\left(x0 \cdot x0\right)}^{3}}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} - {\left({\left(x0 \cdot x0\right)}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(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))