exp-w crasher

Average Error: 0.3 → 0.4

Time: 13.1s

Precision: binary64

• could not determine a ground truth for program body

  1. w = 1.5927317695392267e+246
  2. l = 5.945844110086514e+246

Math

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

↓

\[e^{-w} \cdot {\left({\left({\left({\left({\ell}^{\left(2 \cdot \frac{\left|\sqrt[3]{\sqrt{e^{w}}}\right|}{2}\right)}\right)}^{\left(\sqrt{\sqrt[3]{\sqrt{e^{w}}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\]

Error

Bits error versus w

Bits error versus l

Derivation

1. Initial program 0.3

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

3. Applied add-sqr-sqrt 0.3

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

4. Applied pow-unpow 0.3

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

6. Applied add-sqr-sqrt 0.3

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

7. Applied sqrt-prod 0.3

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

8. Applied pow-unpow 0.3

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

10. Applied add-cube-cbrt 0.3

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

11. Applied sqrt-prod 0.3

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

12. Applied pow-unpow 0.3

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

13. Simplified 0.3

    \[\leadsto e^{-w} \cdot {\left({\left({\color{blue}{\left({\ell}^{\left(2 \cdot \frac{\left|\sqrt[3]{\sqrt{e^{w}}}\right|}{2}\right)}\right)}}^{\left(\sqrt{\sqrt[3]{\sqrt{e^{w}}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{e^{w}}\right)}\]
14. Using strategy rm

15. Applied add-sqr-sqrt 0.3

    \[\leadsto e^{-w} \cdot {\left({\left({\left({\ell}^{\left(2 \cdot \frac{\left|\sqrt[3]{\sqrt{e^{w}}}\right|}{2}\right)}\right)}^{\left(\sqrt{\sqrt[3]{\sqrt{e^{w}}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\color{blue}{\sqrt{e^{w}} \cdot \sqrt{e^{w}}}}\right)}\]

16. Applied sqrt-prod 0.4

    \[\leadsto e^{-w} \cdot {\left({\left({\left({\ell}^{\left(2 \cdot \frac{\left|\sqrt[3]{\sqrt{e^{w}}}\right|}{2}\right)}\right)}^{\left(\sqrt{\sqrt[3]{\sqrt{e^{w}}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\color{blue}{\left(\sqrt{\sqrt{e^{w}}} \cdot \sqrt{\sqrt{e^{w}}}\right)}}\]

17. Applied pow-unpow 0.4

    \[\leadsto e^{-w} \cdot \color{blue}{{\left({\left({\left({\left({\ell}^{\left(2 \cdot \frac{\left|\sqrt[3]{\sqrt{e^{w}}}\right|}{2}\right)}\right)}^{\left(\sqrt{\sqrt[3]{\sqrt{e^{w}}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}}\]

18. Final simplification 0.4

    \[\leadsto e^{-w} \cdot {\left({\left({\left({\left({\ell}^{\left(2 \cdot \frac{\left|\sqrt[3]{\sqrt{e^{w}}}\right|}{2}\right)}\right)}^{\left(\sqrt{\sqrt[3]{\sqrt{e^{w}}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\]

Reproduce

herbie shell --seed 2020175 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (neg w)) (pow l (exp w))))