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

↓

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

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 flip3-+0.3
\[\leadsto \left(\color{blue}{\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log \left(x + y\right) \cdot \log \left(x + y\right) + \left(\log z \cdot \log z - \log \left(x + y\right) \cdot \log z\right)}} - t\right) + \left(a - 0.5\right) \cdot \log t\]
Final simplification0.3
\[\leadsto \left(\frac{{\left(\log \left(y + x\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\left(\log z \cdot \log z - \log \left(y + x\right) \cdot \log z\right) + \log \left(y + x\right) \cdot \log \left(y + x\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]

Reproduce

herbie shell --seed 2019100 
(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))))