Error

Try it out

Derivation

1. Initial program 0.0

   \[e^{re} \cdot \sin im\]

2. Initial simplification0.0

   \[\leadsto \sin im \cdot e^{re}\]
3. Using strategy rm

4. Applied add-sqr-sqrt0.0

   \[\leadsto \sin im \cdot \color{blue}{\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right)}\]

5. Applied associate-*r*0.0

   \[\leadsto \color{blue}{\left(\sin im \cdot \sqrt{e^{re}}\right) \cdot \sqrt{e^{re}}}\]
6. Using strategy rm

7. Applied add-cbrt-cube0.1

   \[\leadsto \left(\sin im \cdot \sqrt{e^{re}}\right) \cdot \color{blue}{\sqrt[3]{\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right) \cdot \sqrt{e^{re}}}}\]
8. Using strategy rm

9. Applied add-cbrt-cube0.1

   \[\leadsto \left(\sin im \cdot \sqrt{e^{re}}\right) \cdot \sqrt[3]{\left(\sqrt{e^{re}} \cdot \color{blue}{\sqrt[3]{\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right) \cdot \sqrt{e^{re}}}}\right) \cdot \sqrt{e^{re}}}\]

10. Applied add-cbrt-cube0.1

    \[\leadsto \left(\sin im \cdot \sqrt{e^{re}}\right) \cdot \sqrt[3]{\left(\color{blue}{\sqrt[3]{\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right) \cdot \sqrt{e^{re}}}} \cdot \sqrt[3]{\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right) \cdot \sqrt{e^{re}}}\right) \cdot \sqrt{e^{re}}}\]

11. Applied cbrt-unprod0.1

    \[\leadsto \left(\sin im \cdot \sqrt{e^{re}}\right) \cdot \sqrt[3]{\color{blue}{\sqrt[3]{\left(\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right) \cdot \sqrt{e^{re}}\right) \cdot \left(\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right) \cdot \sqrt{e^{re}}\right)}} \cdot \sqrt{e^{re}}}\]

12. Simplified0.1

    \[\leadsto \left(\sin im \cdot \sqrt{e^{re}}\right) \cdot \sqrt[3]{\sqrt[3]{\color{blue}{{\left(e^{re}\right)}^{3}}} \cdot \sqrt{e^{re}}}\]

13. Final simplification0.1

    \[\leadsto \left(\sin im \cdot \sqrt{e^{re}}\right) \cdot \sqrt[3]{\sqrt{e^{re}} \cdot \sqrt[3]{{\left(e^{re}\right)}^{3}}}\]

Runtime

Time bar (total: 10.2s)Debug logProfile

herbie shell --seed 2018250 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))