2-ancestry mixing, positive discriminant

1. Initial program 45.1%

   \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
2. Step-by-step derivation

   1. associate-/r*45.1%

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

   2. metadata-eval45.1%

      \[\leadsto \sqrt[3]{\frac{\color{blue}{0.5}}{a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]

   3. +-commutative45.1%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \color{blue}{\left(\sqrt{g \cdot g - h \cdot h} + \left(-g\right)\right)}} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]

   4. unsub-neg45.1%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \color{blue}{\left(\sqrt{g \cdot g - h \cdot h} - g\right)}} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]

   5. fma-neg45.1%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\color{blue}{\mathsf{fma}\left(g, g, -h \cdot h\right)}} - g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]

   6. sub-neg45.1%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \color{blue}{\left(\left(-g\right) + \left(-\sqrt{g \cdot g - h \cdot h}\right)\right)}} \]

   7. distribute-neg-out45.1%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \color{blue}{\left(-\left(g + \sqrt{g \cdot g - h \cdot h}\right)\right)}} \]

   8. neg-mul-145.1%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \color{blue}{\left(-1 \cdot \left(g + \sqrt{g \cdot g - h \cdot h}\right)\right)}} \]

   9. associate-*r*45.1%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)} + \sqrt[3]{\color{blue}{\left(\frac{1}{2 \cdot a} \cdot -1\right) \cdot \left(g + \sqrt{g \cdot g - h \cdot h}\right)}} \]

3. Simplified45.2%

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

   1. associate-*l/45.1%

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

   2. cbrt-div47.8%

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

5. Applied egg-rr48.3%

   \[\leadsto \color{blue}{\frac{\sqrt[3]{0.5 \cdot \left(\mathsf{hypot}\left(g, h\right) - g\right)}}{\sqrt[3]{a}}} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]
6. Step-by-step derivation

   1. cbrt-div48.7%

      \[\leadsto \frac{\sqrt[3]{0.5 \cdot \left(\mathsf{hypot}\left(g, h\right) - g\right)}}{\sqrt[3]{a}} + \color{blue}{\frac{\sqrt[3]{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}}{\sqrt[3]{\frac{a}{-0.5}}}} \]

   2. fma-udef48.7%

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

   3. add-sqr-sqrt26.0%

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

   4. hypot-def43.8%

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

   5. add-sqr-sqrt43.8%

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

   6. sqrt-unprod82.1%

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

   7. sqr-neg82.1%

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

   8. sqrt-unprod89.4%

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

   9. add-sqr-sqrt89.4%

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

   10. sqrt-prod44.2%

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

   11. add-sqr-sqrt95.2%

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

   12. div-inv95.2%

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

   13. metadata-eval95.2%

       \[\leadsto \frac{\sqrt[3]{0.5 \cdot \left(\mathsf{hypot}\left(g, h\right) - g\right)}}{\sqrt[3]{a}} + \frac{\sqrt[3]{g + \mathsf{hypot}\left(g, h\right)}}{\sqrt[3]{a \cdot \color{blue}{-2}}} \]

7. Applied egg-rr95.2%

   \[\leadsto \frac{\sqrt[3]{0.5 \cdot \left(\mathsf{hypot}\left(g, h\right) - g\right)}}{\sqrt[3]{a}} + \color{blue}{\frac{\sqrt[3]{g + \mathsf{hypot}\left(g, h\right)}}{\sqrt[3]{a \cdot -2}}} \]

8. Final simplification95.2%

   \[\leadsto \frac{\sqrt[3]{0.5 \cdot \left(\mathsf{hypot}\left(g, h\right) - g\right)}}{\sqrt[3]{a}} + \frac{\sqrt[3]{g + \mathsf{hypot}\left(g, h\right)}}{\sqrt[3]{a \cdot -2}} \]

1. Initial program 45.1%

   \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
2. Step-by-step derivation

3. Simplified45.1%

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

4. Taylor expanded in g around inf 23.7%

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

5. Taylor expanded in g around inf 74.0%

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

   1. associate-*r/74.0%

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

   2. mul-1-neg74.0%

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

7. Simplified74.0%

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

   1. frac-2neg74.0%

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

   2. cbrt-div95.2%

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

   3. remove-double-neg95.2%

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

9. Applied egg-rr95.2%

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

10. Final simplification95.2%

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

1. Initial program 45.1%

   \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
2. Step-by-step derivation

3. Simplified45.1%

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

4. Taylor expanded in g around inf 23.7%

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

5. Taylor expanded in g around inf 74.0%

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

6. Final simplification74.0%

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

1. Initial program 45.1%

   \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
2. Step-by-step derivation

3. Simplified45.1%

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

4. Taylor expanded in g around inf 23.7%

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

5. Taylor expanded in g around inf 74.0%

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

   1. associate-*r/74.0%

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

   2. mul-1-neg74.0%

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

7. Simplified74.0%

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

8. Final simplification74.0%

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

1. Initial program 45.1%

   \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
2. Step-by-step derivation

3. Simplified45.1%

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

4. Taylor expanded in g around inf 23.7%

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

5. Taylor expanded in g around inf 74.0%

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

   1. associate-*r/74.0%

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

   2. mul-1-neg74.0%

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

7. Simplified74.0%

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

   1. expm1-log1p-u50.4%

      \[\leadsto \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\frac{-g}{a}}\right)\right)} \]

   2. expm1-udef24.9%

      \[\leadsto \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \color{blue}{\left(e^{\mathsf{log1p}\left(\sqrt[3]{\frac{-g}{a}}\right)} - 1\right)} \]

   3. add-sqr-sqrt13.4%

      \[\leadsto \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \left(e^{\mathsf{log1p}\left(\sqrt[3]{\frac{\color{blue}{\sqrt{-g} \cdot \sqrt{-g}}}{a}}\right)} - 1\right) \]

   4. sqrt-unprod8.9%

      \[\leadsto \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \left(e^{\mathsf{log1p}\left(\sqrt[3]{\frac{\color{blue}{\sqrt{\left(-g\right) \cdot \left(-g\right)}}}{a}}\right)} - 1\right) \]

   5. sqr-neg8.9%

      \[\leadsto \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \left(e^{\mathsf{log1p}\left(\sqrt[3]{\frac{\sqrt{\color{blue}{g \cdot g}}}{a}}\right)} - 1\right) \]

   6. sqrt-unprod0.7%

      \[\leadsto \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \left(e^{\mathsf{log1p}\left(\sqrt[3]{\frac{\color{blue}{\sqrt{g} \cdot \sqrt{g}}}{a}}\right)} - 1\right) \]

   7. add-sqr-sqrt1.5%

      \[\leadsto \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \left(e^{\mathsf{log1p}\left(\sqrt[3]{\frac{\color{blue}{g}}{a}}\right)} - 1\right) \]

9. Applied egg-rr1.5%

   \[\leadsto \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \color{blue}{\left(e^{\mathsf{log1p}\left(\sqrt[3]{\frac{g}{a}}\right)} - 1\right)} \]
10. Step-by-step derivation

    1. expm1-def1.1%

       \[\leadsto \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\frac{g}{a}}\right)\right)} \]

    2. expm1-log1p1.4%

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

11. Simplified1.4%

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

12. Final simplification1.4%

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

herbie shell --seed 2023166 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  :precision binary64
  (+ (cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))