Average Error: 0.3 → 0.3
Time: 1.4m
Precision: 64
Internal Precision: 128
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.3

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  2. Initial simplification0.3

    \[\leadsto \log \left(y + x\right) + \left((\left(a - 0.5\right) \cdot \left(\log t\right) + \left(\log z\right))_* - t\right)\]
  3. Using strategy rm

  4. Applied fma-udef0.3

    \[\leadsto \log \left(y + x\right) + \left(\color{blue}{\left(\left(a - 0.5\right) \cdot \log t + \log z\right)} - t\right)\]

  5. Applied associate--l+0.3

    \[\leadsto \log \left(y + x\right) + \color{blue}{\left(\left(a - 0.5\right) \cdot \log t + \left(\log z - t\right)\right)}\]

  6. Applied associate-+r+0.3

    \[\leadsto \color{blue}{\left(\log \left(y + x\right) + \left(a - 0.5\right) \cdot \log t\right) + \left(\log z - t\right)}\]
  7. Using strategy rm

  8. Applied associate-+l+0.3

    \[\leadsto \color{blue}{\log \left(y + x\right) + \left(\left(a - 0.5\right) \cdot \log t + \left(\log z - t\right)\right)}\]

  9. Final simplification0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

Runtime

Time bar (total: 1.4m)Debug logProfile

herbie shell --seed 2018285 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))