exp-w crasher

Average Error: 0.3 → 0.3

Time: 12.4s

Precision: binary64

• could not determine a ground truth for program body

  1. w = 6.619029886509537e+139
  2. l = 3.6471665539575784e+150

Math

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

↓

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

Error

Bits error versus w

Bits error versus l

Derivation

1. Initial program 0.3

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

2. Simplified 0.3

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

4. Applied add-sqr-sqrt 0.3

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

5. Applied pow-unpow 0.3

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

7. Applied add-sqr-sqrt 0.3

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

8. Applied sqrt-prod 0.3

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

9. Applied pow-unpow 0.3

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

10. Final simplification 0.3

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

Reproduce

herbie shell --seed 2020184 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (neg w)) (pow l (exp w))))