Average Error: 0.1 → 0.1
Time: 1.2m
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m - {m}^{3}}{\left(1 + m\right) \cdot v} - 1\right) \cdot \left(1 - m\right)\]

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. Using strategy rm

  3. Applied flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Applied associate-/l/0.1

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

  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. Final simplification0.1

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018336 
(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)))