Average Error: 0.1 → 0.1
Time: 1.4m
Precision: 64
Internal Precision: 576
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[m \cdot \left(1 - \frac{m}{v} \cdot \left(1 - m\right)\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]

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 0.1

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

  2. Initial simplification0.1

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

  4. Applied sub-neg0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Runtime

Time bar (total: 1.4m)Debug logProfile

herbie shell --seed 2018234 
(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)))