Average Error: 0.0 → 0.0
Time: 20.0s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(\frac{\sin re}{e^{im}} + e^{im} \cdot \sin re\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(\frac{\sin re}{e^{im}} + e^{im} \cdot \sin re\right) \cdot 0.5
double f(double re, double im) {
        double r560850 = 0.5;
        double r560851 = re;
        double r560852 = sin(r560851);
        double r560853 = r560850 * r560852;
        double r560854 = 0.0;
        double r560855 = im;
        double r560856 = r560854 - r560855;
        double r560857 = exp(r560856);
        double r560858 = exp(r560855);
        double r560859 = r560857 + r560858;
        double r560860 = r560853 * r560859;
        return r560860;
}
↓
double f(double re, double im) {
        double r560861 = re;
        double r560862 = sin(r560861);
        double r560863 = im;
        double r560864 = exp(r560863);
        double r560865 = r560862 / r560864;
        double r560866 = r560864 * r560862;
        double r560867 = r560865 + r560866;
        double r560868 = 0.5;
        double r560869 = r560867 * r560868;
        return r560869;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))