Average Error: 0.0 → 0.0
Time: 13.8s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \sin im\]
↓
\[\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right) \cdot \sin im\]

Error

Bits error versus re

Bits error versus im

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 associate-*r*0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019072 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))