Average Error: 0.0 → 0.0
Time: 24.4s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r404739 = 0.5;
        double r404740 = re;
        double r404741 = sin(r404740);
        double r404742 = r404739 * r404741;
        double r404743 = 0.0;
        double r404744 = im;
        double r404745 = r404743 - r404744;
        double r404746 = exp(r404745);
        double r404747 = exp(r404744);
        double r404748 = r404746 + r404747;
        double r404749 = r404742 * r404748;
        return r404749;
}
↓
double f(double re, double im) {
        double r404750 = im;
        double r404751 = exp(r404750);
        double r404752 = re;
        double r404753 = sin(r404752);
        double r404754 = r404751 * r404753;
        double r404755 = r404753 / r404751;
        double r404756 = r404754 + r404755;
        double r404757 = 0.5;
        double r404758 = r404756 * r404757;
        return r404758;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{0.5 \cdot \left(\sin re \cdot e^{im} + \frac{\sin re}{e^{im}}\right)}\]

  3. Final simplification0.0

    \[\leadsto \left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]

Reproduce

herbie shell --seed 2019141 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))