Average Error: 0.2 → 0.2
Time: 13.9s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[(\left(\frac{m}{v} \cdot \left(1 - m\right)\right) \cdot m + \left(-m\right))_*\]

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. Simplified0.2

    \[\leadsto \color{blue}{m \cdot (\left(1 - m\right) \cdot \left(\frac{m}{v}\right) + -1)_*}\]
  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 fma-def0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019026 +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))