Error

Derivation

1. Initial program 0.0

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

3. Applied add-sqr-sqrt0.0

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

4. Applied associate-*l*0.0

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

6. Applied add-cube-cbrt0.1

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

8. Applied add-cube-cbrt0.1

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

9. Applied sqrt-prod0.1

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

10. Applied cbrt-prod0.1

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

11. Applied add-cube-cbrt0.1

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

12. Applied sqrt-prod0.1

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

13. Applied cbrt-prod0.1

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

14. Applied swap-sqr0.1

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

15. Applied associate-*l*0.1

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

16. Applied associate-*l*0.1

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

17. Simplified0.1

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

18. Final simplification0.1

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

Reproduce

herbie shell --seed 2019088 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))