Average Error: 0.2 → 0.2
Time: 35.7s
Precision: 64
Internal Precision: 320
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\left(\frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right)\]

Error

Bits error versus m

Bits error versus v

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded around 0 0.2

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

  3. Final simplification0.2

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

Runtime

Time bar (total: 35.7s)Debug logProfile

herbie shell --seed 2018251 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))