Average Error: 0.2 → 0.2
Time: 38.6s
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. Using strategy rm

  3. Applied flip3--0.2

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

  4. Applied associate-*r/0.7

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

  5. Applied associate-/l/0.7

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

  6. Simplified0.7

    \[\leadsto \left(\frac{\color{blue}{m - {m}^{4}}}{v \cdot \left(1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)\right)} - 1\right) \cdot m\]

  7. Taylor expanded around inf 6.7

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

  9. Applied unpow26.7

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

  10. Applied associate-/l*0.2

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

  11. Final simplification0.2

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

Runtime

Time bar (total: 38.6s)Debug logProfile

herbie shell --seed 2018254 +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))