Average Error: 0.0 → 0.0
Time: 29.0s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{\sin re}{e^{im}} \cdot 0.5 + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{\sin re}{e^{im}} \cdot 0.5 + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r18805 = 0.5;
        double r18806 = re;
        double r18807 = sin(r18806);
        double r18808 = r18805 * r18807;
        double r18809 = 0.0;
        double r18810 = im;
        double r18811 = r18809 - r18810;
        double r18812 = exp(r18811);
        double r18813 = exp(r18810);
        double r18814 = r18812 + r18813;
        double r18815 = r18808 * r18814;
        return r18815;
}
↓
double f(double re, double im) {
        double r18816 = re;
        double r18817 = sin(r18816);
        double r18818 = im;
        double r18819 = exp(r18818);
        double r18820 = r18817 / r18819;
        double r18821 = 0.5;
        double r18822 = r18820 * r18821;
        double r18823 = r18821 * r18817;
        double r18824 = r18823 * r18819;
        double r18825 = r18822 + r18824;
        return r18825;
}

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

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))