Average Error: 0.0 → 0.0
Time: 13.5s
Precision: 64
Internal Precision: 576
\[e^{re} \cdot \sin im\]
↓
\[\left(\left(\sqrt{e^{re \cdot \frac{2}{3}}} \cdot \sin im\right) \cdot \sqrt{e^{re \cdot \frac{2}{3}}}\right) \cdot \sqrt[3]{e^{re}}\]

Error

Bits error versus re

Bits error versus im

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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-cube-cbrt0.1

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

  5. Applied associate-*r*0.1

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

  6. Taylor expanded around inf 0.0

    \[\leadsto \color{blue}{\left(\sin im \cdot {\left(e^{\frac{1}{3} \cdot re}\right)}^{2}\right)} \cdot \sqrt[3]{e^{re}}\]

  7. Simplified0.0

    \[\leadsto \color{blue}{\left(\sin im \cdot e^{re \cdot \frac{2}{3}}\right)} \cdot \sqrt[3]{e^{re}}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt0.0

    \[\leadsto \left(\sin im \cdot \color{blue}{\left(\sqrt{e^{re \cdot \frac{2}{3}}} \cdot \sqrt{e^{re \cdot \frac{2}{3}}}\right)}\right) \cdot \sqrt[3]{e^{re}}\]

  10. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(\left(\sin im \cdot \sqrt{e^{re \cdot \frac{2}{3}}}\right) \cdot \sqrt{e^{re \cdot \frac{2}{3}}}\right)} \cdot \sqrt[3]{e^{re}}\]

  11. Final simplification0.0

    \[\leadsto \left(\left(\sqrt{e^{re \cdot \frac{2}{3}}} \cdot \sin im\right) \cdot \sqrt{e^{re \cdot \frac{2}{3}}}\right) \cdot \sqrt[3]{e^{re}}\]

Runtime

Time bar (total: 13.5s)Debug logProfile

herbie shell --seed 2018235 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))