Average Error: 0.0 → 0.0
Time: 28.8s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \frac{\sin re}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
0.5 \cdot \frac{\sin re}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r17765 = 0.5;
        double r17766 = re;
        double r17767 = sin(r17766);
        double r17768 = r17765 * r17767;
        double r17769 = 0.0;
        double r17770 = im;
        double r17771 = r17769 - r17770;
        double r17772 = exp(r17771);
        double r17773 = exp(r17770);
        double r17774 = r17772 + r17773;
        double r17775 = r17768 * r17774;
        return r17775;
}
↓
double f(double re, double im) {
        double r17776 = 0.5;
        double r17777 = re;
        double r17778 = sin(r17777);
        double r17779 = im;
        double r17780 = exp(r17779);
        double r17781 = r17778 / r17780;
        double r17782 = r17776 * r17781;
        double r17783 = r17776 * r17778;
        double r17784 = r17783 * r17780;
        double r17785 = r17782 + r17784;
        return r17785;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Taylor expanded around inf 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))