(- (/ 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 = 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

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

↓

\[\begin{array}{l} \mathbf{if}\;x1 \le 4.024513549804687 \cdot 10^{-4}:\\ \;\;\;\;\frac{\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{6} + \left(-{\left(x0 \cdot x0\right)}^{6}\right)}{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} + {\left(x0 \cdot x0\right)}^{3}}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} - {\left({\left(x0 \cdot x0\right)}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \end{array}\]

C

double f(double x0, double x1) {
        double r166775 = x0;
        double r166776 = 1.0;
        double r166777 = x1;
        double r166778 = r166776 - r166777;
        double r166779 = r166775 / r166778;
        double r166780 = r166779 - r166775;
        return r166780;
}

↓

double f(double x0, double x1) {
        double r166781 = x1;
        double r166782 = 0.0004024513549804687;
        bool r166783 = r166781 <= r166782;
        double r166784 = x0;
        double r166785 = cbrt(r166784);
        double r166786 = r166785 * r166785;
        double r166787 = 1.0;
        double r166788 = r166787 - r166781;
        double r166789 = sqrt(r166788);
        double r166790 = r166786 / r166789;
        double r166791 = r166785 / r166789;
        double r166792 = r166790 * r166791;
        double r166793 = r166784 / r166788;
        double r166794 = r166792 * r166793;
        double r166795 = 6.0;
        double r166796 = pow(r166794, r166795);
        double r166797 = r166784 * r166784;
        double r166798 = pow(r166797, r166795);
        double r166799 = -r166798;
        double r166800 = r166796 + r166799;
        double r166801 = 3.0;
        double r166802 = pow(r166794, r166801);
        double r166803 = pow(r166797, r166801);
        double r166804 = r166802 + r166803;
        double r166805 = r166800 / r166804;
        double r166806 = 2.0;
        double r166807 = pow(r166784, r166806);
        double r166808 = r166807 + r166794;
        double r166809 = r166807 * r166808;
        double r166810 = r166794 * r166794;
        double r166811 = r166809 + r166810;
        double r166812 = r166805 / r166811;
        double r166813 = r166793 + r166784;
        double r166814 = r166812 / r166813;
        double r166815 = sqrt(r166801);
        double r166816 = pow(r166797, r166815);
        double r166817 = pow(r166816, r166815);
        double r166818 = r166802 - r166817;
        double r166819 = r166818 / r166811;
        double r166820 = r166819 / r166813;
        double r166821 = r166783 ? r166814 : r166820;
        return r166821;
}

Error

Bits error versus x0

Bits error versus x1

Target

Original	7.9
Target	0.3
Herbie	3.9

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

Derivation

1. Split input into 2 regimes

2. if x1 < 0.0004024513549804687

   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 0.0004024513549804687 < x1

   1. Initial program 4.6

      \[\frac{x0}{1 - x1} - x0\]
   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-- 5.2

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

   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 2.3

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

   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

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \le 4.024513549804687 \cdot 10^{-4}:\\ \;\;\;\;\frac{\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{6} + \left(-{\left(x0 \cdot x0\right)}^{6}\right)}{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} + {\left(x0 \cdot x0\right)}^{3}}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} - {\left({\left(x0 \cdot x0\right)}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(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))