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

↓

\[\left(\sqrt[3]{{\left(\log z + \log \left(y + x\right)\right)}^{3}} - t\right) + \left(a - 0.5\right) \cdot \log t\]

Error

The X axis uses an exponential scale — Bits error versus `x`

Derivation

Initial program 0.3
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
Using strategy rm
Applied add-cbrt-cube0.3
\[\leadsto \left(\color{blue}{\sqrt[3]{\left(\left(\log \left(x + y\right) + \log z\right) \cdot \left(\log \left(x + y\right) + \log z\right)\right) \cdot \left(\log \left(x + y\right) + \log z\right)}} - t\right) + \left(a - 0.5\right) \cdot \log t\]
Applied simplify0.3
\[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\log z + \log \left(y + x\right)\right)}^{3}}} - t\right) + \left(a - 0.5\right) \cdot \log t\]

Runtime

herbie shell --seed '#(1064397287 3527694221 3797617954 1138343853 2854031332 1153838279)' 
(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))))