Average Error: 0.2 → 0.3
Time: 41.3s
Precision: 64
Internal Precision: 1600
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
\[e^{-w} \cdot {\left({\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\]

Error

Bits error versus w

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

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

    \[\leadsto e^{-w} \cdot {\ell}^{\color{blue}{\left(\sqrt{e^{w}} \cdot \sqrt{e^{w}}\right)}}\]
  4. Applied pow-unpow0.3

    \[\leadsto e^{-w} \cdot \color{blue}{{\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left(\sqrt{e^{w}}\right)}}\]
  5. Using strategy rm
  6. Applied add-sqr-sqrt0.3

    \[\leadsto e^{-w} \cdot {\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left(\sqrt{\color{blue}{\sqrt{e^{w}} \cdot \sqrt{e^{w}}}}\right)}\]
  7. Applied sqrt-prod0.3

    \[\leadsto e^{-w} \cdot {\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\color{blue}{\left(\sqrt{\sqrt{e^{w}}} \cdot \sqrt{\sqrt{e^{w}}}\right)}}\]
  8. Applied pow-unpow0.3

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

Runtime

Time bar (total: 41.3s)Debug log

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