exp-w crasher

Average Error: 0.3 → 0.4

Time: 13.5s

Precision: binary64

• could not determine a ground truth for program body

  1. w = 7.545945601055156e+229
  2. l = -1.6240242067751955e-246

Math

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

↓

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

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-cube-cbrt 0.4

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

7. Applied sqrt-prod 0.4

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

8. Applied pow-unpow 0.4

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

9. Simplified 0.4

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

11. Applied pow1/3 0.4

    \[\leadsto e^{-w} \cdot {\left({\left({\ell}^{\left(\left|\sqrt[3]{e^{w}}\right|\right)}\right)}^{\left(\sqrt{\color{blue}{{\left(e^{w}\right)}^{\frac{1}{3}}}}\right)}\right)}^{\left(\sqrt{e^{w}}\right)}\]
12. Using strategy rm

13. Applied add-cube-cbrt 0.4

    \[\leadsto e^{-w} \cdot {\left({\left({\ell}^{\left(\left|\sqrt[3]{e^{w}}\right|\right)}\right)}^{\left(\sqrt{{\left(e^{w}\right)}^{\frac{1}{3}}}\right)}\right)}^{\color{blue}{\left(\left(\sqrt[3]{\sqrt{e^{w}}} \cdot \sqrt[3]{\sqrt{e^{w}}}\right) \cdot \sqrt[3]{\sqrt{e^{w}}}\right)}}\]

14. Applied pow-unpow 0.4

    \[\leadsto e^{-w} \cdot \color{blue}{{\left({\left({\left({\ell}^{\left(\left|\sqrt[3]{e^{w}}\right|\right)}\right)}^{\left(\sqrt{{\left(e^{w}\right)}^{\frac{1}{3}}}\right)}\right)}^{\left(\sqrt[3]{\sqrt{e^{w}}} \cdot \sqrt[3]{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt[3]{\sqrt{e^{w}}}\right)}}\]

15. Simplified 0.4

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

16. Final simplification 0.4

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

Reproduce

herbie shell --seed 2020181 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (neg w)) (pow l (exp w))))