Average Error: 0.1 → 0.6
Time: 6.9m
Precision: 64
Internal Precision: 576
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[(\left(\frac{\left({1}^{3} - {m}^{3}\right) \cdot \left(1 - m\right)}{(m \cdot \left(m + 1\right) + 1)_*}\right) \cdot \left(\frac{m}{v}\right) + \left(-\left(1 - m\right)\right))_*\]

Error

Bits error versus m

Bits error versus v

Derivation

  1. Initial program 0.1

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

  2. Initial simplification0.1

    \[\leadsto (\left(\left(1 - m\right) \cdot \left(1 - m\right)\right) \cdot \left(\frac{m}{v}\right) + \left(-\left(1 - m\right)\right))_*\]
  3. Using strategy rm

  4. Applied flip3--0.1

    \[\leadsto (\left(\left(1 - m\right) \cdot \color{blue}{\frac{{1}^{3} - {m}^{3}}{1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)}}\right) \cdot \left(\frac{m}{v}\right) + \left(-\left(1 - m\right)\right))_*\]

  5. Applied associate-*r/0.6

    \[\leadsto (\color{blue}{\left(\frac{\left(1 - m\right) \cdot \left({1}^{3} - {m}^{3}\right)}{1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)}\right)} \cdot \left(\frac{m}{v}\right) + \left(-\left(1 - m\right)\right))_*\]

  6. Simplified0.6

    \[\leadsto (\left(\frac{\left(1 - m\right) \cdot \left({1}^{3} - {m}^{3}\right)}{\color{blue}{(m \cdot \left(1 + m\right) + 1)_*}}\right) \cdot \left(\frac{m}{v}\right) + \left(-\left(1 - m\right)\right))_*\]

  7. Final simplification0.6

    \[\leadsto (\left(\frac{\left({1}^{3} - {m}^{3}\right) \cdot \left(1 - m\right)}{(m \cdot \left(m + 1\right) + 1)_*}\right) \cdot \left(\frac{m}{v}\right) + \left(-\left(1 - m\right)\right))_*\]

Runtime

Time bar (total: 6.9m)Debug logProfile

herbie shell --seed 2018217 +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)))