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Derivation

1. Initial program 0.1

   \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]

2. Taylor expanded around -inf 0.1

   \[\leadsto \left(\color{blue}{\left(\frac{m}{v} - \frac{{m}^{2}}{v}\right)} - 1\right) \cdot \left(1 - m\right)\]
3. Using strategy rm

4. Applied clear-num0.1

   \[\leadsto \left(\left(\frac{m}{v} - \color{blue}{\frac{1}{\frac{v}{{m}^{2}}}}\right) - 1\right) \cdot \left(1 - m\right)\]

5. Final simplification0.1

   \[\leadsto \left(\left(\frac{m}{v} - \frac{1}{\frac{v}{{m}^{2}}}\right) - 1\right) \cdot \left(1 - m\right)\]

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018263 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))