Average Error: 0.2 → 0.2
Time: 22.6s
Precision: 64
Internal Precision: 576
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(1 - m\right) \cdot \frac{m}{\frac{v}{m}} - m\]

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

    \[\leadsto \frac{m - m \cdot m}{\frac{v}{m}} - m\]
  3. Using strategy rm

  4. Applied sub-neg0.2

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

  6. Applied *-un-lft-identity0.2

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

  7. Applied distribute-lft-neg-in0.2

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

  8. Applied distribute-rgt1-in0.2

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

  9. Applied times-frac0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Runtime

Time bar (total: 22.6s)Debug logProfile

herbie shell --seed 2018256 
(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))