Average Error: 0.3 → 0.3
Time: 55.7s
Precision: 64
Internal Precision: 576
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log t \cdot \left(a - 0.5\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 *-commutative0.3

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

  4. Final simplification0.3

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

Runtime

Time bar (total: 55.7s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.30.30.10.20%
herbie shell --seed 2018290 +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))))