Average Error: 0.1 → 0.1
Time: 1.1m
Precision: 64
Internal Precision: 576
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{v} + \left(m \cdot \frac{m}{v}\right) \cdot \left(m - 2\right)\right) - \left(1 - m\right)\]

Error

Bits error versus m

Bits error versus v

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Your Program's Arguments

Results

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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. Initial simplification0.2

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018249 
(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)))