exp-w crasher

Average Error: 0.3 → 0.6

Time: 15.8s

Precision: binary64

• could not determine a ground truth for program body

  1. w = 1.35448315408323e+61
  2. l = -9.17574089558758e-243

Math

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

↓

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

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 0.3

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

5. Applied add-sqr-sqrt 0.6

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

6. Applied times-frac 0.6

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

7. Final simplification 0.6

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

Reproduce

herbie shell --seed 2020171 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (neg w)) (pow l (exp w))))