Average Error: 0.2 → 0.2
Time: 18.4s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m - {m}^{2}}{v} - 1\right) \cdot m\]

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. Taylor expanded around -inf 0.2

    \[\leadsto \left(\frac{\color{blue}{m - {m}^{2}}}{v} - 1\right) \cdot m\]

  3. Final simplification0.2

    \[\leadsto \left(\frac{m - {m}^{2}}{v} - 1\right) \cdot m\]

Runtime

Time bar (total: 18.4s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.20.20.00.10%
herbie shell --seed 2018353 +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))