Average Error: 0.0 → 0.1
Time: 3.7s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[{\left(\sqrt{\sqrt{e^{re}}}\right)}^{3} \cdot \left(\sqrt{\sqrt{e^{re}}} \cdot \sin im\right)\]
e^{re} \cdot \sin im
↓
{\left(\sqrt{\sqrt{e^{re}}}\right)}^{3} \cdot \left(\sqrt{\sqrt{e^{re}}} \cdot \sin im\right)
double f(double re, double im) {
        double r39720 = re;
        double r39721 = exp(r39720);
        double r39722 = im;
        double r39723 = sin(r39722);
        double r39724 = r39721 * r39723;
        return r39724;
}
↓
double f(double re, double im) {
        double r39725 = re;
        double r39726 = exp(r39725);
        double r39727 = sqrt(r39726);
        double r39728 = sqrt(r39727);
        double r39729 = 3.0;
        double r39730 = pow(r39728, r39729);
        double r39731 = im;
        double r39732 = sin(r39731);
        double r39733 = r39728 * r39732;
        double r39734 = r39730 * r39733;
        return r39734;
}

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

    \[e^{re} \cdot \sin im\]
  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-sqr-sqrt0.0

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

  7. Applied sqrt-prod0.1

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

  8. Applied associate-*l*0.1

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

  10. Applied associate-*r*0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019344 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))