exp-w crasher

Average Error: 0.3 → 0.3

Time: 12.8s

Precision: binary64

• could not determine a ground truth for program body

  1. w = 2.30262976956565e+132
  2. l = -4.123489692462463e-37

Math

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

↓

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

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-cube-cbrt 0.3

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

4. Applied associate-*l* 0.3

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

5. Final simplification 0.3

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

Reproduce

herbie shell --seed 2020173 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (neg w)) (pow l (exp w))))