Average Error: 0.3 → 0.3
Time: 2.0m
Precision: 64
Internal Precision: 384
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(y + x\right) - \left(t - (\left(a - 0.5\right) \cdot \left(\log t\right) + \left(\log z\right))_*\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

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. Applied simplify0.3

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

Runtime

Time bar (total: 2.0m)Debug logProfile

herbie shell --seed '#(1070833653 108281690 3330367898 3632331308 3494323072 43156186)' +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))))