Average Error: 0.2 → 0.5
Time: 58.3s
Precision: 64
Internal Precision: 1344
\[e^{y} \cdot {\ell}^{\left(e^{-y}\right)}\]
\[\sqrt{e^{y} \cdot {\ell}^{\left(e^{-y}\right)}} \cdot \sqrt{e^{y} \cdot {\left({\ell}^{\left(\sqrt{e^{-y}}\right)}\right)}^{\left(\sqrt{e^{-y}}\right)}}\]

Error

Bits error versus y

Bits error versus l

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[e^{y} \cdot {\ell}^{\left(e^{-y}\right)}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt0.5

    \[\leadsto \color{blue}{\sqrt{e^{y} \cdot {\ell}^{\left(e^{-y}\right)}} \cdot \sqrt{e^{y} \cdot {\ell}^{\left(e^{-y}\right)}}}\]
  4. Using strategy rm
  5. Applied add-sqr-sqrt0.5

    \[\leadsto \sqrt{e^{y} \cdot {\ell}^{\left(e^{-y}\right)}} \cdot \sqrt{e^{y} \cdot {\ell}^{\color{blue}{\left(\sqrt{e^{-y}} \cdot \sqrt{e^{-y}}\right)}}}\]
  6. Applied pow-unpow0.5

    \[\leadsto \sqrt{e^{y} \cdot {\ell}^{\left(e^{-y}\right)}} \cdot \sqrt{e^{y} \cdot \color{blue}{{\left({\ell}^{\left(\sqrt{e^{-y}}\right)}\right)}^{\left(\sqrt{e^{-y}}\right)}}}\]

Runtime

Time bar (total: 58.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (y l)
  :name "exp(y) * l ^ (exp(-y))"
  (* (exp y) (pow l (exp (- y)))))