Average Error: 0.0 → 0.0
Time: 16.7s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(\frac{1}{2} \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(\frac{1}{2} \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
double f(double re, double im) {
        double r16735 = 0.5;
        double r16736 = re;
        double r16737 = sin(r16736);
        double r16738 = r16735 * r16737;
        double r16739 = 0.0;
        double r16740 = im;
        double r16741 = r16739 - r16740;
        double r16742 = exp(r16741);
        double r16743 = exp(r16740);
        double r16744 = r16742 + r16743;
        double r16745 = r16738 * r16744;
        return r16745;
}
↓
double f(double re, double im) {
        double r16746 = 1.0;
        double r16747 = 2.0;
        double r16748 = r16746 / r16747;
        double r16749 = re;
        double r16750 = sin(r16749);
        double r16751 = r16748 * r16750;
        double r16752 = 0.0;
        double r16753 = im;
        double r16754 = r16752 - r16753;
        double r16755 = exp(r16754);
        double r16756 = exp(r16753);
        double r16757 = r16755 + r16756;
        double r16758 = r16751 * r16757;
        return r16758;
}

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

    \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)}\]

  3. Final simplification0.0

    \[\leadsto \left(\frac{1}{2} \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]

Reproduce

herbie shell --seed 2019303 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))