exp-w crasher

Average Error: 0.2 → 0.3

Time: 13.0s

Precision: binary64

• could not determine a ground truth for program body

  1. w = 5.435531754509878e+163
  2. l = 1.4370837309570488e+51

Math

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

↓

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

Error

Bits error versus w

Bits error versus l

Derivation

1. Initial program 0.2

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
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 0.3

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

7. Applied associate-*l* 0.3

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

8. Final simplification 0.3

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

Reproduce

herbie shell --seed 2020174 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (neg w)) (pow l (exp w))))