Average Error: 0.1 → 0.1
Time: 1.1m
Precision: 64
Internal Precision: 576
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m - {m}^{3}}{v \cdot m + v} - 1\right) \cdot \left(1 - m\right)\]

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. Initial simplification0.1

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

  4. Applied flip--0.1

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

  5. Applied frac-times0.1

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

  6. Simplified0.1

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

  7. Taylor expanded around inf 0.1

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

  8. Final simplification0.1

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

Runtime

Time bar (total: 1.1m)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)))