2-ancestry mixing, zero discriminant

1. Initial program 75.9%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Step-by-step derivation

   1. cbrt-div98.8%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}} \]

   2. div-inv98.8%

      \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}} \]

3. Applied egg-rr98.8%

   \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}} \]
4. Step-by-step derivation

   1. associate-*r/98.8%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{g} \cdot 1}{\sqrt[3]{2 \cdot a}}} \]

   2. *-rgt-identity98.8%

      \[\leadsto \frac{\color{blue}{\sqrt[3]{g}}}{\sqrt[3]{2 \cdot a}} \]

   3. *-commutative98.8%

      \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{\color{blue}{a \cdot 2}}} \]

5. Simplified98.8%

   \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}}} \]
6. Step-by-step derivation

   1. /-rgt-identity98.8%

      \[\leadsto \frac{\sqrt[3]{g}}{\color{blue}{\frac{\sqrt[3]{a \cdot 2}}{1}}} \]

   2. clear-num98.8%

      \[\leadsto \frac{\sqrt[3]{g}}{\color{blue}{\frac{1}{\frac{1}{\sqrt[3]{a \cdot 2}}}}} \]

   3. clear-num98.8%

      \[\leadsto \frac{\sqrt[3]{g}}{\frac{1}{\color{blue}{\frac{1}{\frac{\sqrt[3]{a \cdot 2}}{1}}}}} \]

   4. metadata-eval98.8%

      \[\leadsto \frac{\sqrt[3]{g}}{\frac{1}{\frac{\color{blue}{\sqrt[3]{1}}}{\frac{\sqrt[3]{a \cdot 2}}{1}}}} \]

   5. /-rgt-identity98.8%

      \[\leadsto \frac{\sqrt[3]{g}}{\frac{1}{\frac{\sqrt[3]{1}}{\color{blue}{\sqrt[3]{a \cdot 2}}}}} \]

   6. metadata-eval98.8%

      \[\leadsto \frac{\sqrt[3]{g}}{\frac{1}{\frac{\sqrt[3]{1}}{\sqrt[3]{a \cdot \color{blue}{\frac{1}{0.5}}}}}} \]

   7. div-inv98.8%

      \[\leadsto \frac{\sqrt[3]{g}}{\frac{1}{\frac{\sqrt[3]{1}}{\sqrt[3]{\color{blue}{\frac{a}{0.5}}}}}} \]

   8. cbrt-div98.8%

      \[\leadsto \frac{\sqrt[3]{g}}{\frac{1}{\color{blue}{\sqrt[3]{\frac{1}{\frac{a}{0.5}}}}}} \]

   9. clear-num98.8%

      \[\leadsto \frac{\sqrt[3]{g}}{\frac{1}{\sqrt[3]{\color{blue}{\frac{0.5}{a}}}}} \]

7. Applied egg-rr98.8%

   \[\leadsto \frac{\sqrt[3]{g}}{\color{blue}{\frac{1}{\sqrt[3]{\frac{0.5}{a}}}}} \]

8. Final simplification98.8%

   \[\leadsto \frac{\sqrt[3]{g}}{\frac{1}{\sqrt[3]{\frac{0.5}{a}}}} \]

1. Initial program 75.9%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Step-by-step derivation

   1. div-inv75.9%

      \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}} \]

   2. cbrt-prod98.7%

      \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}} \]

   3. associate-/r*98.7%

      \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\color{blue}{\frac{\frac{1}{2}}{a}}} \]

   4. metadata-eval98.7%

      \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{\color{blue}{0.5}}{a}} \]

3. Applied egg-rr98.7%

   \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{a}}} \]

4. Final simplification98.7%

   \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{a}} \]

1. Initial program 75.9%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Step-by-step derivation

   1. cbrt-div98.8%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}} \]

   2. div-inv98.8%

      \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}} \]

3. Applied egg-rr98.8%

   \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}} \]
4. Step-by-step derivation

   1. associate-*r/98.8%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{g} \cdot 1}{\sqrt[3]{2 \cdot a}}} \]

   2. *-rgt-identity98.8%

      \[\leadsto \frac{\color{blue}{\sqrt[3]{g}}}{\sqrt[3]{2 \cdot a}} \]

   3. *-commutative98.8%

      \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{\color{blue}{a \cdot 2}}} \]

5. Simplified98.8%

   \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}}} \]

6. Final simplification98.8%

   \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}} \]

1. Initial program 75.9%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Step-by-step derivation

   1. expm1-log1p-u57.8%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)\right)} \]

   2. expm1-udef22.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)} - 1} \]

   3. log1p-udef22.6%

      \[\leadsto e^{\color{blue}{\log \left(1 + \sqrt[3]{\frac{g}{2 \cdot a}}\right)}} - 1 \]

   4. add-exp-log40.7%

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

   5. *-un-lft-identity40.7%

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

   6. times-frac40.7%

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

   7. metadata-eval40.7%

      \[\leadsto \left(1 + \sqrt[3]{\color{blue}{0.5} \cdot \frac{g}{a}}\right) - 1 \]

3. Applied egg-rr40.7%

   \[\leadsto \color{blue}{\left(1 + \sqrt[3]{0.5 \cdot \frac{g}{a}}\right) - 1} \]
4. Step-by-step derivation

   1. +-commutative40.7%

      \[\leadsto \color{blue}{\left(\sqrt[3]{0.5 \cdot \frac{g}{a}} + 1\right)} - 1 \]

   2. associate--l+75.9%

      \[\leadsto \color{blue}{\sqrt[3]{0.5 \cdot \frac{g}{a}} + \left(1 - 1\right)} \]

   3. metadata-eval75.9%

      \[\leadsto \sqrt[3]{0.5 \cdot \frac{g}{a}} + \color{blue}{0} \]

   4. +-rgt-identity75.9%

      \[\leadsto \color{blue}{\sqrt[3]{0.5 \cdot \frac{g}{a}}} \]

   5. associate-*r/75.9%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{0.5 \cdot g}{a}}} \]

   6. associate-*l/75.9%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{0.5}{a} \cdot g}} \]

5. Simplified75.9%

   \[\leadsto \color{blue}{\sqrt[3]{\frac{0.5}{a} \cdot g}} \]
6. Step-by-step derivation

   1. associate-*l/75.9%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{0.5 \cdot g}{a}}} \]

   2. clear-num75.4%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{1}{\frac{a}{0.5 \cdot g}}}} \]

   3. *-commutative75.4%

      \[\leadsto \sqrt[3]{\frac{1}{\frac{a}{\color{blue}{g \cdot 0.5}}}} \]

   4. metadata-eval75.4%

      \[\leadsto \sqrt[3]{\frac{1}{\frac{a}{g \cdot \color{blue}{\frac{1}{2}}}}} \]

   5. div-inv75.4%

      \[\leadsto \sqrt[3]{\frac{1}{\frac{a}{\color{blue}{\frac{g}{2}}}}} \]

   6. un-div-inv75.5%

      \[\leadsto \sqrt[3]{\frac{1}{\color{blue}{a \cdot \frac{1}{\frac{g}{2}}}}} \]

   7. clear-num75.5%

      \[\leadsto \sqrt[3]{\frac{1}{a \cdot \color{blue}{\frac{2}{g}}}} \]

7. Applied egg-rr75.5%

   \[\leadsto \sqrt[3]{\color{blue}{\frac{1}{a \cdot \frac{2}{g}}}} \]
8. Step-by-step derivation

   1. frac-2neg75.5%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{-1}{-a \cdot \frac{2}{g}}}} \]

   2. metadata-eval75.5%

      \[\leadsto \sqrt[3]{\frac{\color{blue}{-1}}{-a \cdot \frac{2}{g}}} \]

   3. div-inv75.5%

      \[\leadsto \sqrt[3]{\color{blue}{-1 \cdot \frac{1}{-a \cdot \frac{2}{g}}}} \]

   4. distribute-rgt-neg-in75.5%

      \[\leadsto \sqrt[3]{-1 \cdot \frac{1}{\color{blue}{a \cdot \left(-\frac{2}{g}\right)}}} \]

9. Applied egg-rr75.5%

   \[\leadsto \sqrt[3]{\color{blue}{-1 \cdot \frac{1}{a \cdot \left(-\frac{2}{g}\right)}}} \]

11. Simplified75.9%

    \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{-1}{a}}{\frac{-2}{g}}}} \]

12. Final simplification75.9%

    \[\leadsto \sqrt[3]{\frac{\frac{-1}{a}}{\frac{-2}{g}}} \]

1. Split input into 2 regimes

2. if a < -3.999999999999988e-310

   1. Initial program 77.3%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   2. Step-by-step derivation

      1. clear-num76.5%

         \[\leadsto \sqrt[3]{\color{blue}{\frac{1}{\frac{2 \cdot a}{g}}}} \]

      2. cbrt-div76.7%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{\frac{2 \cdot a}{g}}}} \]

      3. metadata-eval76.7%

         \[\leadsto \frac{\color{blue}{1}}{\sqrt[3]{\frac{2 \cdot a}{g}}} \]

      4. *-un-lft-identity76.7%

         \[\leadsto \frac{1}{\sqrt[3]{\frac{2 \cdot a}{\color{blue}{1 \cdot g}}}} \]

      5. times-frac76.5%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2}{1} \cdot \frac{a}{g}}}} \]

      6. metadata-eval76.5%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{2} \cdot \frac{a}{g}}} \]

   3. Applied egg-rr76.5%

      \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{2 \cdot \frac{a}{g}}}} \]
   4. Step-by-step derivation

      1. associate-*r/76.7%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2 \cdot a}{g}}}} \]

      2. associate-*l/76.6%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2}{g} \cdot a}}} \]

   5. Simplified76.6%

      \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{\frac{2}{g} \cdot a}}} \]
   6. Step-by-step derivation

      1. associate-*l/76.7%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2 \cdot a}{g}}}} \]

      2. *-commutative76.7%

         \[\leadsto \frac{1}{\sqrt[3]{\frac{\color{blue}{a \cdot 2}}{g}}} \]

      3. cbrt-div98.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{a \cdot 2}}{\sqrt[3]{g}}}} \]

      4. div-inv98.6%

         \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{a \cdot 2} \cdot \frac{1}{\sqrt[3]{g}}}} \]

      5. metadata-eval98.6%

         \[\leadsto \frac{1}{\sqrt[3]{a \cdot \color{blue}{\frac{1}{0.5}}} \cdot \frac{1}{\sqrt[3]{g}}} \]

      6. div-inv98.6%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{a}{0.5}}} \cdot \frac{1}{\sqrt[3]{g}}} \]

      7. add-log-exp1.9%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\log \left(e^{\frac{a}{0.5}}\right)}} \cdot \frac{1}{\sqrt[3]{g}}} \]

      8. div-inv1.9%

         \[\leadsto \frac{1}{\sqrt[3]{\log \left(e^{\color{blue}{a \cdot \frac{1}{0.5}}}\right)} \cdot \frac{1}{\sqrt[3]{g}}} \]

      9. metadata-eval1.9%

         \[\leadsto \frac{1}{\sqrt[3]{\log \left(e^{a \cdot \color{blue}{2}}\right)} \cdot \frac{1}{\sqrt[3]{g}}} \]

      10. exp-lft-sqr1.9%

          \[\leadsto \frac{1}{\sqrt[3]{\log \color{blue}{\left(e^{a} \cdot e^{a}\right)}} \cdot \frac{1}{\sqrt[3]{g}}} \]

      11. log-prod1.9%

          \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\log \left(e^{a}\right) + \log \left(e^{a}\right)}} \cdot \frac{1}{\sqrt[3]{g}}} \]

      12. add-log-exp12.8%

          \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{a} + \log \left(e^{a}\right)} \cdot \frac{1}{\sqrt[3]{g}}} \]

      13. add-log-exp98.6%

          \[\leadsto \frac{1}{\sqrt[3]{a + \color{blue}{a}} \cdot \frac{1}{\sqrt[3]{g}}} \]

   7. Applied egg-rr98.6%

      \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{a + a} \cdot \frac{1}{\sqrt[3]{g}}}} \]
   8. Step-by-step derivation

      1. associate-*r/98.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{a + a} \cdot 1}{\sqrt[3]{g}}}} \]

      2. *-rgt-identity98.6%

         \[\leadsto \frac{1}{\frac{\color{blue}{\sqrt[3]{a + a}}}{\sqrt[3]{g}}} \]

   9. Simplified98.6%

      \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{g}}}} \]
   10. Step-by-step derivation

       1. clear-num98.6%

          \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{a + a}}} \]

       2. cbrt-undiv77.3%

          \[\leadsto \color{blue}{\sqrt[3]{\frac{g}{a + a}}} \]

       3. flip-+0.0%

          \[\leadsto \sqrt[3]{\frac{g}{\color{blue}{\frac{a \cdot a - a \cdot a}{a - a}}}} \]

       4. +-inverses0.0%

          \[\leadsto \sqrt[3]{\frac{g}{\frac{\color{blue}{0}}{a - a}}} \]

       5. +-inverses0.0%

          \[\leadsto \sqrt[3]{\frac{g}{\frac{0}{\color{blue}{0}}}} \]

   11. Applied egg-rr0.0%

       \[\leadsto \color{blue}{\sqrt[3]{\frac{g}{\frac{0}{0}}}} \]

   13. Simplified7.6%

       \[\leadsto \color{blue}{\sqrt[3]{\frac{g}{-1}}} \]

   if -3.999999999999988e-310 < a

   1. Initial program 74.7%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   2. Step-by-step derivation

      1. clear-num74.6%

         \[\leadsto \sqrt[3]{\color{blue}{\frac{1}{\frac{2 \cdot a}{g}}}} \]

      2. cbrt-div75.2%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{\frac{2 \cdot a}{g}}}} \]

      3. metadata-eval75.2%

         \[\leadsto \frac{\color{blue}{1}}{\sqrt[3]{\frac{2 \cdot a}{g}}} \]

      4. *-un-lft-identity75.2%

         \[\leadsto \frac{1}{\sqrt[3]{\frac{2 \cdot a}{\color{blue}{1 \cdot g}}}} \]

      5. times-frac75.2%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2}{1} \cdot \frac{a}{g}}}} \]

      6. metadata-eval75.2%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{2} \cdot \frac{a}{g}}} \]

   3. Applied egg-rr75.2%

      \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{2 \cdot \frac{a}{g}}}} \]
   4. Step-by-step derivation

      1. associate-*r/75.2%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2 \cdot a}{g}}}} \]

      2. associate-*l/75.1%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2}{g} \cdot a}}} \]

   5. Simplified75.1%

      \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{\frac{2}{g} \cdot a}}} \]
   6. Step-by-step derivation

      1. associate-*l/75.2%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2 \cdot a}{g}}}} \]

      2. *-commutative75.2%

         \[\leadsto \frac{1}{\sqrt[3]{\frac{\color{blue}{a \cdot 2}}{g}}} \]

      3. cbrt-div98.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{a \cdot 2}}{\sqrt[3]{g}}}} \]

      4. div-inv98.8%

         \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{a \cdot 2} \cdot \frac{1}{\sqrt[3]{g}}}} \]

      5. metadata-eval98.8%

         \[\leadsto \frac{1}{\sqrt[3]{a \cdot \color{blue}{\frac{1}{0.5}}} \cdot \frac{1}{\sqrt[3]{g}}} \]

      6. div-inv98.8%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{a}{0.5}}} \cdot \frac{1}{\sqrt[3]{g}}} \]

      7. add-log-exp5.1%

         \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\log \left(e^{\frac{a}{0.5}}\right)}} \cdot \frac{1}{\sqrt[3]{g}}} \]

      8. div-inv5.1%

         \[\leadsto \frac{1}{\sqrt[3]{\log \left(e^{\color{blue}{a \cdot \frac{1}{0.5}}}\right)} \cdot \frac{1}{\sqrt[3]{g}}} \]

      9. metadata-eval5.1%

         \[\leadsto \frac{1}{\sqrt[3]{\log \left(e^{a \cdot \color{blue}{2}}\right)} \cdot \frac{1}{\sqrt[3]{g}}} \]

      10. exp-lft-sqr5.0%

          \[\leadsto \frac{1}{\sqrt[3]{\log \color{blue}{\left(e^{a} \cdot e^{a}\right)}} \cdot \frac{1}{\sqrt[3]{g}}} \]

      11. log-prod5.0%

          \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\log \left(e^{a}\right) + \log \left(e^{a}\right)}} \cdot \frac{1}{\sqrt[3]{g}}} \]

      12. add-log-exp13.5%

          \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{a} + \log \left(e^{a}\right)} \cdot \frac{1}{\sqrt[3]{g}}} \]

      13. add-log-exp98.8%

          \[\leadsto \frac{1}{\sqrt[3]{a + \color{blue}{a}} \cdot \frac{1}{\sqrt[3]{g}}} \]

   7. Applied egg-rr98.8%

      \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{a + a} \cdot \frac{1}{\sqrt[3]{g}}}} \]
   8. Step-by-step derivation

      1. associate-*r/98.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{a + a} \cdot 1}{\sqrt[3]{g}}}} \]

      2. *-rgt-identity98.9%

         \[\leadsto \frac{1}{\frac{\color{blue}{\sqrt[3]{a + a}}}{\sqrt[3]{g}}} \]

   9. Simplified98.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{g}}}} \]
   10. Step-by-step derivation

       1. expm1-log1p-u73.1%

          \[\leadsto \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sqrt[3]{a + a}}{\sqrt[3]{g}}\right)\right)}} \]

       2. expm1-udef39.6%

          \[\leadsto \frac{1}{\color{blue}{e^{\mathsf{log1p}\left(\frac{\sqrt[3]{a + a}}{\sqrt[3]{g}}\right)} - 1}} \]

   11. Applied egg-rr0.0%

       \[\leadsto \frac{1}{\color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{0}{0}}{\sqrt[3]{g}}\right)} - 1}} \]

   13. Simplified6.0%

       \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{g}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification6.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\sqrt[3]{\frac{g}{-1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt[3]{g}}\\ \end{array} \]

1. Initial program 75.9%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Step-by-step derivation

   1. expm1-log1p-u57.8%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)\right)} \]

   2. expm1-udef22.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)} - 1} \]

   3. log1p-udef22.6%

      \[\leadsto e^{\color{blue}{\log \left(1 + \sqrt[3]{\frac{g}{2 \cdot a}}\right)}} - 1 \]

   4. add-exp-log40.7%

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

   5. *-un-lft-identity40.7%

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

   6. times-frac40.7%

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

   7. metadata-eval40.7%

      \[\leadsto \left(1 + \sqrt[3]{\color{blue}{0.5} \cdot \frac{g}{a}}\right) - 1 \]

3. Applied egg-rr40.7%

   \[\leadsto \color{blue}{\left(1 + \sqrt[3]{0.5 \cdot \frac{g}{a}}\right) - 1} \]
4. Step-by-step derivation

   1. +-commutative40.7%

      \[\leadsto \color{blue}{\left(\sqrt[3]{0.5 \cdot \frac{g}{a}} + 1\right)} - 1 \]

   2. associate--l+75.9%

      \[\leadsto \color{blue}{\sqrt[3]{0.5 \cdot \frac{g}{a}} + \left(1 - 1\right)} \]

   3. metadata-eval75.9%

      \[\leadsto \sqrt[3]{0.5 \cdot \frac{g}{a}} + \color{blue}{0} \]

   4. +-rgt-identity75.9%

      \[\leadsto \color{blue}{\sqrt[3]{0.5 \cdot \frac{g}{a}}} \]

   5. associate-*r/75.9%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{0.5 \cdot g}{a}}} \]

   6. associate-*l/75.9%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{0.5}{a} \cdot g}} \]

5. Simplified75.9%

   \[\leadsto \color{blue}{\sqrt[3]{\frac{0.5}{a} \cdot g}} \]

6. Final simplification75.9%

   \[\leadsto \sqrt[3]{g \cdot \frac{0.5}{a}} \]

1. Initial program 75.9%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Step-by-step derivation

   1. clear-num75.4%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{1}{\frac{2 \cdot a}{g}}}} \]

   2. cbrt-div75.8%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{\frac{2 \cdot a}{g}}}} \]

   3. metadata-eval75.8%

      \[\leadsto \frac{\color{blue}{1}}{\sqrt[3]{\frac{2 \cdot a}{g}}} \]

   4. *-un-lft-identity75.8%

      \[\leadsto \frac{1}{\sqrt[3]{\frac{2 \cdot a}{\color{blue}{1 \cdot g}}}} \]

   5. times-frac75.8%

      \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2}{1} \cdot \frac{a}{g}}}} \]

   6. metadata-eval75.8%

      \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{2} \cdot \frac{a}{g}}} \]

3. Applied egg-rr75.8%

   \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{2 \cdot \frac{a}{g}}}} \]
4. Step-by-step derivation

   1. associate-*r/75.8%

      \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2 \cdot a}{g}}}} \]

   2. associate-*l/75.8%

      \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2}{g} \cdot a}}} \]

5. Simplified75.8%

   \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{\frac{2}{g} \cdot a}}} \]
6. Step-by-step derivation

   1. associate-*l/75.8%

      \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2 \cdot a}{g}}}} \]

   2. *-commutative75.8%

      \[\leadsto \frac{1}{\sqrt[3]{\frac{\color{blue}{a \cdot 2}}{g}}} \]

   3. cbrt-div98.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{a \cdot 2}}{\sqrt[3]{g}}}} \]

   4. div-inv98.7%

      \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{a \cdot 2} \cdot \frac{1}{\sqrt[3]{g}}}} \]

   5. metadata-eval98.7%

      \[\leadsto \frac{1}{\sqrt[3]{a \cdot \color{blue}{\frac{1}{0.5}}} \cdot \frac{1}{\sqrt[3]{g}}} \]

   6. div-inv98.7%

      \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{a}{0.5}}} \cdot \frac{1}{\sqrt[3]{g}}} \]

   7. add-log-exp3.7%

      \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\log \left(e^{\frac{a}{0.5}}\right)}} \cdot \frac{1}{\sqrt[3]{g}}} \]

   8. div-inv3.7%

      \[\leadsto \frac{1}{\sqrt[3]{\log \left(e^{\color{blue}{a \cdot \frac{1}{0.5}}}\right)} \cdot \frac{1}{\sqrt[3]{g}}} \]

   9. metadata-eval3.7%

      \[\leadsto \frac{1}{\sqrt[3]{\log \left(e^{a \cdot \color{blue}{2}}\right)} \cdot \frac{1}{\sqrt[3]{g}}} \]

   10. exp-lft-sqr3.7%

       \[\leadsto \frac{1}{\sqrt[3]{\log \color{blue}{\left(e^{a} \cdot e^{a}\right)}} \cdot \frac{1}{\sqrt[3]{g}}} \]

   11. log-prod3.7%

       \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\log \left(e^{a}\right) + \log \left(e^{a}\right)}} \cdot \frac{1}{\sqrt[3]{g}}} \]

   12. add-log-exp13.2%

       \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{a} + \log \left(e^{a}\right)} \cdot \frac{1}{\sqrt[3]{g}}} \]

   13. add-log-exp98.7%

       \[\leadsto \frac{1}{\sqrt[3]{a + \color{blue}{a}} \cdot \frac{1}{\sqrt[3]{g}}} \]

7. Applied egg-rr98.7%

   \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{a + a} \cdot \frac{1}{\sqrt[3]{g}}}} \]
8. Step-by-step derivation

   1. associate-*r/98.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{a + a} \cdot 1}{\sqrt[3]{g}}}} \]

   2. *-rgt-identity98.8%

      \[\leadsto \frac{1}{\frac{\color{blue}{\sqrt[3]{a + a}}}{\sqrt[3]{g}}} \]

9. Simplified98.8%

   \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{g}}}} \]
10. Step-by-step derivation

    1. clear-num98.8%

       \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{a + a}}} \]

    2. cbrt-undiv75.9%

       \[\leadsto \color{blue}{\sqrt[3]{\frac{g}{a + a}}} \]

    3. flip-+0.0%

       \[\leadsto \sqrt[3]{\frac{g}{\color{blue}{\frac{a \cdot a - a \cdot a}{a - a}}}} \]

    4. +-inverses0.0%

       \[\leadsto \sqrt[3]{\frac{g}{\frac{\color{blue}{0}}{a - a}}} \]

    5. +-inverses0.0%

       \[\leadsto \sqrt[3]{\frac{g}{\frac{0}{\color{blue}{0}}}} \]

11. Applied egg-rr0.0%

    \[\leadsto \color{blue}{\sqrt[3]{\frac{g}{\frac{0}{0}}}} \]

13. Simplified4.3%

    \[\leadsto \color{blue}{\sqrt[3]{\frac{g}{-1}}} \]

14. Final simplification4.3%

    \[\leadsto \sqrt[3]{\frac{g}{-1}} \]

herbie shell --seed 2023167 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))