Average Error: 0.3 → 0.5
Time: 3.2m
Precision: 64
Internal Precision: 384
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\sqrt[3]{\log \left(x + y\right) + \log z} \cdot \sqrt[3]{\log \left(x + y\right) + \log z}\right) \cdot \sqrt[3]{\log \left(x + y\right) + \log z} - t\right) + \left(a - 0.5\right) \cdot \log t\]

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. Using strategy rm

  3. Applied add-cube-cbrt0.5

    \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\log \left(x + y\right) + \log z} \cdot \sqrt[3]{\log \left(x + y\right) + \log z}\right) \cdot \sqrt[3]{\log \left(x + y\right) + \log z}} - t\right) + \left(a - 0.5\right) \cdot \log t\]
  4. Removed slow pow expressions.

Runtime

Time bar (total: 3.2m)Debug logProfile

herbie shell --seed '#(1063282112 2455465480 4141627379 3773598652 1647277307 776739644)' 
(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))))