Average Error: 0.3 → 0.7
Time: 1.6m
Precision: 64
Internal Precision: 576
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\sqrt[3]{a - 0.5} \cdot \sqrt[3]{\log t}\right) \cdot \left(\sqrt[3]{\left(a - 0.5\right) \cdot \log t} \cdot \sqrt[3]{\left(a - 0.5\right) \cdot \log t}\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]

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 add-cube-cbrt0.7

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\left(\sqrt[3]{\left(a - 0.5\right) \cdot \log t} \cdot \sqrt[3]{\left(a - 0.5\right) \cdot \log t}\right) \cdot \sqrt[3]{\left(a - 0.5\right) \cdot \log t}}\]
  4. Using strategy rm

  5. Applied cbrt-prod0.7

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

  6. Final simplification0.7

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

Runtime

Time bar (total: 1.6m)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.70.70.00.60%
herbie shell --seed 2018263 
(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))))