Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\left(\left|\sqrt[3]{e^{re}}\right| \cdot \sqrt{\sqrt[3]{e^{re}}}\right) \cdot \left(\sqrt{\sqrt{e^{re}}} \cdot \left(\sqrt{\sqrt{e^{re}}} \cdot \cos im\right)\right)\]
e^{re} \cdot \cos im
↓
\left(\left|\sqrt[3]{e^{re}}\right| \cdot \sqrt{\sqrt[3]{e^{re}}}\right) \cdot \left(\sqrt{\sqrt{e^{re}}} \cdot \left(\sqrt{\sqrt{e^{re}}} \cdot \cos im\right)\right)
double code(double re, double im) {
	return (exp(re) * cos(im));
}
↓
double code(double re, double im) {
	return ((fabs(cbrt(exp(re))) * sqrt(cbrt(exp(re)))) * (sqrt(sqrt(exp(re))) * (sqrt(sqrt(exp(re))) * cos(im))));
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*l*0.0

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

  6. Applied add-cube-cbrt0.0

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

  7. Applied sqrt-prod0.0

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

  8. Simplified0.0

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

  10. Applied add-sqr-sqrt0.0

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

  11. Applied sqrt-prod0.0

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

  12. Applied associate-*l*0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2020078 
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))