\[e^{re} \cdot \sin im\]

↓

\[\sin im \cdot e^{re}\]

e^{re} \cdot \sin im

↓

\sin im \cdot e^{re}

double f(double re, double im) {
        double r1923742 = re;
        double r1923743 = exp(r1923742);
        double r1923744 = im;
        double r1923745 = sin(r1923744);
        double r1923746 = r1923743 * r1923745;
        return r1923746;
}

↓

double f(double re, double im) {
        double r1923747 = im;
        double r1923748 = sin(r1923747);
        double r1923749 = re;
        double r1923750 = exp(r1923749);
        double r1923751 = r1923748 * r1923750;
        return r1923751;
}

Try it out

In
Out

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Derivation

Initial program 0.0
\[e^{re} \cdot \sin im\]
Final simplification0.0
\[\leadsto \sin im \cdot e^{re}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Error

Try it out

Derivation

Reproduce