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

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.2

$e^{-w} \cdot {\ell}^{\left(e^{w}\right)}$
2. Using strategy rm

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

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