Average Error: 0.1 → 0.1
Time: 3.0m
Precision: 64
Internal Precision: 576
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\frac{m}{v} \cdot \left(1 - m\right) + \left(\left(m - 1\right) - \frac{m}{v} \cdot \left(m - m \cdot m\right)\right)\]

Error

Bits error versus m

Bits error versus v

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 sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Applied simplify0.1

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

  6. Applied simplify0.1

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

  8. Applied sub-neg0.1

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

  9. Applied associate-+l+0.1

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

  10. Applied simplify0.1

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

Runtime

Time bar (total: 3.0m)Debug logProfile

herbie shell --seed '#(1071852389 864846987 1238109217 3425890003 4124793586 650694553)' 
(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)))