Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[\sqrt{e^{re}} \cdot \left({\left(e^{1}\right)}^{\left(\frac{1}{2} \cdot re\right)} \cdot \sin im\right)\]
e^{re} \cdot \sin im
↓
\sqrt{e^{re}} \cdot \left({\left(e^{1}\right)}^{\left(\frac{1}{2} \cdot re\right)} \cdot \sin im\right)
double f(double re, double im) {
        double r34331 = re;
        double r34332 = exp(r34331);
        double r34333 = im;
        double r34334 = sin(r34333);
        double r34335 = r34332 * r34334;
        return r34335;
}
↓
double f(double re, double im) {
        double r34336 = re;
        double r34337 = exp(r34336);
        double r34338 = sqrt(r34337);
        double r34339 = 1.0;
        double r34340 = exp(r34339);
        double r34341 = 0.5;
        double r34342 = r34341 * r34336;
        double r34343 = pow(r34340, r34342);
        double r34344 = im;
        double r34345 = sin(r34344);
        double r34346 = r34343 * r34345;
        double r34347 = r34338 * r34346;
        return r34347;
}

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 *-un-lft-identity0.0

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

  7. Applied exp-prod0.0

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

  8. Applied sqrt-pow10.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))