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

↓

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

Error

The X axis uses an exponential scale — Bits error versus `g`

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In
Out

Enter valid numbers for all inputs

Derivation

Initial program 35.4
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
Initial simplification35.4
\[\leadsto \sqrt[3]{\frac{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g}{a \cdot 2}} + \sqrt[3]{\frac{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{a \cdot 2}}\]
Final simplification35.4
\[\leadsto \sqrt[3]{\frac{\left(-g\right) - \sqrt{\left(h + g\right) \cdot \left(g - h\right)}}{2 \cdot a}} + \sqrt[3]{\frac{\sqrt{\left(h + g\right) \cdot \left(g - h\right)} - g}{2 \cdot a}}\]

Runtime

herbie shell --seed 2018215 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))