Average Error: 0.2 → 0.2
Time: 1.1m
Precision: 64
Internal Precision: 384
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
\[\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot m\]

Error

Bits error versus m

Bits error versus v

Derivation

  1. Initial program 0.2

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
  2. Using strategy rm
  3. Applied flip--0.2

    \[\leadsto \left(\frac{m \cdot \color{blue}{\frac{1 \cdot 1 - m \cdot m}{1 + m}}}{v} - 1\right) \cdot m\]
  4. Applied associate-*r/0.2

    \[\leadsto \left(\frac{\color{blue}{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}}{v} - 1\right) \cdot m\]
  5. Applied associate-/l/0.2

    \[\leadsto \left(\color{blue}{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)}} - 1\right) \cdot m\]
  6. Using strategy rm
  7. Applied flip-+0.2

    \[\leadsto \left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \color{blue}{\frac{1 \cdot 1 - m \cdot m}{1 - m}}} - 1\right) \cdot m\]
  8. Applied associate-*r/0.2

    \[\leadsto \left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{\color{blue}{\frac{v \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 - m}}} - 1\right) \cdot m\]
  9. Applied associate-/r/0.2

    \[\leadsto \left(\color{blue}{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 \cdot 1 - m \cdot m\right)} \cdot \left(1 - m\right)} - 1\right) \cdot m\]
  10. Applied simplify0.2

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed '#(1070609872 3456127585 2380521889 2328837196 1765472538 734540918)' 
(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))