Average Error: 0.3 → 0.6
Time: 1.8m
Precision: 64
Internal Precision: 576
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot {\left(\log t \cdot \log t\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\log t}\]

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

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

  4. Applied associate-*r*0.7

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

  6. Applied pow1/331.9

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(\sqrt[3]{\log t} \cdot \color{blue}{{\left(\log t\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\log t}\]

  7. Applied pow1/331.9

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(\color{blue}{{\left(\log t\right)}^{\frac{1}{3}}} \cdot {\left(\log t\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\log t}\]

  8. Applied pow-prod-down0.6

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \color{blue}{{\left(\log t \cdot \log t\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\log t}\]

Runtime

Time bar (total: 1.8m)Debug logProfile

herbie shell --seed 2018195 
(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))))