Average Error: 0.0 → 0.0
Time: 19.5s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[\left(\sqrt{e^{re}} \cdot \sin im\right) \cdot {e}^{\left(\frac{re}{2}\right)}\]
e^{re} \cdot \sin im
↓
\left(\sqrt{e^{re}} \cdot \sin im\right) \cdot {e}^{\left(\frac{re}{2}\right)}
double f(double re, double im) {
        double r46984 = re;
        double r46985 = exp(r46984);
        double r46986 = im;
        double r46987 = sin(r46986);
        double r46988 = r46985 * r46987;
        return r46988;
}
↓
double f(double re, double im) {
        double r46989 = re;
        double r46990 = exp(r46989);
        double r46991 = sqrt(r46990);
        double r46992 = im;
        double r46993 = sin(r46992);
        double r46994 = r46991 * r46993;
        double r46995 = exp(1.0);
        double r46996 = 2.0;
        double r46997 = r46989 / r46996;
        double r46998 = pow(r46995, r46997);
        double r46999 = r46994 * r46998;
        return r46999;
}

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

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

  7. Applied exp-prod0.0

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

  8. Applied sqrt-pow10.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))