Average Error: 0.2 → 0.2
Time: 46.6s
Precision: 64
Internal Precision: 320
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m}{\frac{v}{m}} - \left(m + \frac{{m}^{3}}{v}\right)\]

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 -inf 6.8

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

  4. Applied unpow26.8

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

  5. Applied associate-/l*0.2

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

  6. Final simplification0.2

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

Runtime

Time bar (total: 46.6s)Debug logProfile

herbie shell --seed 2018251 +o rules:numerics
(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))