exp-w crasher

Average Error: 0.3 → 1.3

Time: 15.9s

Precision: binary64

• could not determine a ground truth for program body

  1. w = 2.0849792867836596e+232
  2. l = 1.267400067230941e+159

Math

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

↓

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

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-cube-cbrt 1.3

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

5. Final simplification 1.3

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

Reproduce

herbie shell --seed 2020169 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (neg w)) (pow l (exp w))))