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

Average Error: 7.9 → 3.9

Time: 4.4s

Precision: 64

• could not determine a ground truth for program pre

  1. x0 = 2.985
  2. x1 = 0.000209

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

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 r175606 = x0;
        double r175607 = 1.0;
        double r175608 = x1;
        double r175609 = r175607 - r175608;
        double r175610 = r175606 / r175609;
        double r175611 = r175610 - r175606;
        return r175611;
}

↓

double f(double x0, double x1) {
        double r175612 = x1;
        double r175613 = 0.00021208908081054686;
        bool r175614 = r175612 <= r175613;
        double r175615 = x0;
        double r175616 = cbrt(r175615);
        double r175617 = r175616 * r175616;
        double r175618 = 1.0;
        double r175619 = r175618 - r175612;
        double r175620 = sqrt(r175619);
        double r175621 = r175617 / r175620;
        double r175622 = r175616 / r175620;
        double r175623 = r175621 * r175622;
        double r175624 = r175615 / r175619;
        double r175625 = r175623 * r175624;
        double r175626 = 6.0;
        double r175627 = pow(r175625, r175626);
        double r175628 = r175615 * r175615;
        double r175629 = pow(r175628, r175626);
        double r175630 = -r175629;
        double r175631 = r175627 + r175630;
        double r175632 = 3.0;
        double r175633 = pow(r175625, r175632);
        double r175634 = pow(r175628, r175632);
        double r175635 = r175633 + r175634;
        double r175636 = r175631 / r175635;
        double r175637 = 2.0;
        double r175638 = pow(r175615, r175637);
        double r175639 = r175638 + r175625;
        double r175640 = r175638 * r175639;
        double r175641 = r175625 * r175625;
        double r175642 = r175640 + r175641;
        double r175643 = r175636 / r175642;
        double r175644 = r175624 + r175615;
        double r175645 = r175643 / r175644;
        double r175646 = sqrt(r175632);
        double r175647 = pow(r175628, r175646);
        double r175648 = pow(r175647, r175646);
        double r175649 = r175633 - r175648;
        double r175650 = r175649 / r175642;
        double r175651 = r175650 / r175644;
        double r175652 = r175614 ? r175645 : r175651;
        return r175652;
}

Error

Bits error versus x0

Bits error versus x1

Target

Original	7.9
Target	0.2
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 8.0

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

   6. Applied add-cube-cbrt 8.0

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

   7. Applied times-frac 8.0

      \[\leadsto \frac{\color{blue}{\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right)} \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}\]
   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-- 7.7

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

   13. Simplified 7.2

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

   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 2020020 
(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))