Average Error: 0.0 → 0.0
Time: 33.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(\frac{\sin re}{e^{im}} + e^{im} \cdot \sin re\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - 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 r928712 = 0.5;
        double r928713 = re;
        double r928714 = sin(r928713);
        double r928715 = r928712 * r928714;
        double r928716 = 0.0;
        double r928717 = im;
        double r928718 = r928716 - r928717;
        double r928719 = exp(r928718);
        double r928720 = exp(r928717);
        double r928721 = r928719 + r928720;
        double r928722 = r928715 * r928721;
        return r928722;
}
↓
double f(double re, double im) {
        double r928723 = re;
        double r928724 = sin(r928723);
        double r928725 = im;
        double r928726 = exp(r928725);
        double r928727 = r928724 / r928726;
        double r928728 = r928726 * r928724;
        double r928729 = r928727 + r928728;
        double r928730 = 0.5;
        double r928731 = r928729 * r928730;
        return r928731;
}

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. Taylor expanded around inf 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))