Average Error: 0.3 → 0.3
Time: 11.8s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\frac{{\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left(\log \left(e^{\sqrt{e^{w}}}\right)\right)}}{e^{w}}\]

Error

Bits error versus w

Bits error versus l

Derivation

  1. Initial program 0.3

    \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.3

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

  5. Applied pow-unpow0.3

    \[\leadsto \frac{\color{blue}{{\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left(\sqrt{e^{w}}\right)}}}{e^{w}}\]
  6. Using strategy rm

  7. Applied add-log-exp0.3

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

  8. Final simplification0.3

    \[\leadsto \frac{{\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left(\log \left(e^{\sqrt{e^{w}}}\right)\right)}}{e^{w}}\]

Reproduce

herbie shell --seed 2020185 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (neg w)) (pow l (exp w))))