Average Error: 0.0 → 0.0
Time: 2.4m
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \sin re}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\frac{0.5 \cdot \sin re}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r14826776 = 0.5;
        double r14826777 = re;
        double r14826778 = sin(r14826777);
        double r14826779 = r14826776 * r14826778;
        double r14826780 = 0.0;
        double r14826781 = im;
        double r14826782 = r14826780 - r14826781;
        double r14826783 = exp(r14826782);
        double r14826784 = exp(r14826781);
        double r14826785 = r14826783 + r14826784;
        double r14826786 = r14826779 * r14826785;
        return r14826786;
}
↓
double f(double re, double im) {
        double r14826787 = 0.5;
        double r14826788 = re;
        double r14826789 = sin(r14826788);
        double r14826790 = r14826787 * r14826789;
        double r14826791 = im;
        double r14826792 = exp(r14826791);
        double r14826793 = r14826790 / r14826792;
        double r14826794 = r14826790 * r14826792;
        double r14826795 = r14826793 + r14826794;
        return r14826795;
}

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

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

  3. Taylor expanded around -inf 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))