Average Error: 0.3 → 0.3
Time: 44.8s
Precision: 64
Internal Precision: 128
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log \left(x + y\right) + \left(a - 0.5\right) \cdot \log t\right) - \left(t - \log z\right)\]

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

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

  3. Taylor expanded around inf 0.3

    \[\leadsto \left(\log \left(y + x\right) + \color{blue}{\left(0.5 \cdot \log \left(\frac{1}{t}\right) - a \cdot \log \left(\frac{1}{t}\right)\right)}\right) - \left(t - \log z\right)\]

  4. Simplified0.3

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

  5. Final simplification0.3

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

Runtime

Time bar (total: 44.8s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.30.30.00.20%
herbie shell --seed 2018353 
(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))))