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

↓

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

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-cube-cbrt0.4
\[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\log \left(x + y\right)} \cdot \sqrt[3]{\log \left(x + y\right)}\right) \cdot \sqrt[3]{\log \left(x + y\right)}} + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
Applied fma-def0.4
\[\leadsto \left(\color{blue}{(\left(\sqrt[3]{\log \left(x + y\right)} \cdot \sqrt[3]{\log \left(x + y\right)}\right) \cdot \left(\sqrt[3]{\log \left(x + y\right)}\right) + \left(\log z\right))_*} - t\right) + \left(a - 0.5\right) \cdot \log t\]

Runtime

herbie shell --seed '#(1070258749 1877548225 2229079127 1588002776 3179087814 1886870650)' +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))))