Average Error: 0.2 → 0.2
Time: 41.8s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(\left(1 - m\right) \cdot m\right) \cdot \frac{1}{v}\right) \cdot m + \left(-m\right)\]

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 0.2

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

  2. Initial simplification0.2

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

  4. Applied fma-udef0.2

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

  5. Applied distribute-rgt-in0.2

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

  6. Simplified0.2

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

  8. Applied div-inv0.2

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

  9. Applied associate-*r*0.2

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

  10. Final simplification0.2

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

Runtime

Time bar (total: 41.8s)Debug logProfile

herbie shell --seed 2018277 +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))