Average Error: 0.1 → 0.1
Time: 45.2s
Precision: 64
Internal Precision: 320
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) + \left(\frac{m}{v} \cdot \left(m \cdot m - m\right) + m\right)\]

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 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

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

  4. Applied distribute-rgt-in0.1

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

  5. Simplified0.1

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

  6. Taylor expanded around -inf 0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Runtime

Time bar (total: 45.2s)Debug logProfile

herbie shell --seed 2018248 
(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)))