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

Average Error: 7.9 → 3.9

Time: 4.7s

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

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

↓

\[\begin{array}{l} \mathbf{if}\;1 - x1 \le 0.99059549999999996:\\ \;\;\;\;\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} - {\left({\left(x0 \cdot x0\right)}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{6} + \left(-{\left(x0 \cdot x0\right)}^{6}\right)}{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} + {\left(x0 \cdot x0\right)}^{3}}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \end{array}\]

C

double f(double x0, double x1) {
        double r206937 = x0;
        double r206938 = 1.0;
        double r206939 = x1;
        double r206940 = r206938 - r206939;
        double r206941 = r206937 / r206940;
        double r206942 = r206941 - r206937;
        return r206942;
}

↓

double f(double x0, double x1) {
        double r206943 = 1.0;
        double r206944 = x1;
        double r206945 = r206943 - r206944;
        double r206946 = 0.9905955;
        bool r206947 = r206945 <= r206946;
        double r206948 = x0;
        double r206949 = cbrt(r206948);
        double r206950 = r206949 * r206949;
        double r206951 = sqrt(r206945);
        double r206952 = r206950 / r206951;
        double r206953 = r206949 / r206951;
        double r206954 = r206952 * r206953;
        double r206955 = r206948 / r206945;
        double r206956 = r206954 * r206955;
        double r206957 = 3.0;
        double r206958 = pow(r206956, r206957);
        double r206959 = r206948 * r206948;
        double r206960 = sqrt(r206957);
        double r206961 = pow(r206959, r206960);
        double r206962 = pow(r206961, r206960);
        double r206963 = r206958 - r206962;
        double r206964 = 2.0;
        double r206965 = pow(r206948, r206964);
        double r206966 = r206965 + r206956;
        double r206967 = r206965 * r206966;
        double r206968 = r206956 * r206956;
        double r206969 = r206967 + r206968;
        double r206970 = r206963 / r206969;
        double r206971 = r206955 + r206948;
        double r206972 = r206970 / r206971;
        double r206973 = 6.0;
        double r206974 = pow(r206956, r206973);
        double r206975 = pow(r206959, r206973);
        double r206976 = -r206975;
        double r206977 = r206974 + r206976;
        double r206978 = pow(r206959, r206957);
        double r206979 = r206958 + r206978;
        double r206980 = r206977 / r206979;
        double r206981 = r206980 / r206969;
        double r206982 = r206981 / r206971;
        double r206983 = r206947 ? r206972 : r206982;
        return r206983;
}

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 (- 1.0 x1) < 0.9905955

   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

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

   if 0.9905955 < (- 1.0 x1)

   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

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

4. Final simplification 3.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - x1 \le 0.99059549999999996:\\ \;\;\;\;\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} - {\left({\left(x0 \cdot x0\right)}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{6} + \left(-{\left(x0 \cdot x0\right)}^{6}\right)}{{\left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}^{3} + {\left(x0 \cdot x0\right)}^{3}}}{{x0}^{2} \cdot \left({x0}^{2} + \left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) + \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right) \cdot \left(\left(\frac{\sqrt[3]{x0} \cdot \sqrt[3]{x0}}{\sqrt{1 - x1}} \cdot \frac{\sqrt[3]{x0}}{\sqrt{1 - x1}}\right) \cdot \frac{x0}{1 - x1}\right)}}{\frac{x0}{1 - x1} + x0}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(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))