Average Error: 0.0 → 0.0
Time: 18.4s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r908158 = 0.5;
        double r908159 = re;
        double r908160 = sin(r908159);
        double r908161 = r908158 * r908160;
        double r908162 = 0.0;
        double r908163 = im;
        double r908164 = r908162 - r908163;
        double r908165 = exp(r908164);
        double r908166 = exp(r908163);
        double r908167 = r908165 + r908166;
        double r908168 = r908161 * r908167;
        return r908168;
}
↓
double f(double re, double im) {
        double r908169 = im;
        double r908170 = exp(r908169);
        double r908171 = re;
        double r908172 = sin(r908171);
        double r908173 = r908170 * r908172;
        double r908174 = r908172 / r908170;
        double r908175 = r908173 + r908174;
        double r908176 = 0.5;
        double r908177 = r908175 * r908176;
        return r908177;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019192 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))