Average Error: 0.0 → 0.0
Time: 18.3s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
double f(double re, double im) {
        double r18683 = 0.5;
        double r18684 = re;
        double r18685 = sin(r18684);
        double r18686 = r18683 * r18685;
        double r18687 = 0.0;
        double r18688 = im;
        double r18689 = r18687 - r18688;
        double r18690 = exp(r18689);
        double r18691 = exp(r18688);
        double r18692 = r18690 + r18691;
        double r18693 = r18686 * r18692;
        return r18693;
}
↓
double f(double re, double im) {
        double r18694 = 0.5;
        double r18695 = re;
        double r18696 = sin(r18695);
        double r18697 = r18694 * r18696;
        double r18698 = 0.0;
        double r18699 = im;
        double r18700 = r18698 - r18699;
        double r18701 = exp(r18700);
        double r18702 = exp(r18699);
        double r18703 = r18701 + r18702;
        double r18704 = r18697 * r18703;
        return r18704;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(\sin re \cdot 0.5\right) \cdot \left(e^{0.0 - im} + e^{im}\right)}\]

  3. Final simplification0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]

Reproduce

herbie shell --seed 2019196 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))