Average Error: 0.0 → 0.0
Time: 21.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(\sin re \cdot e^{im} + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(\sin re \cdot e^{im} + \frac{\sin re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r896464 = 0.5;
        double r896465 = re;
        double r896466 = sin(r896465);
        double r896467 = r896464 * r896466;
        double r896468 = 0.0;
        double r896469 = im;
        double r896470 = r896468 - r896469;
        double r896471 = exp(r896470);
        double r896472 = exp(r896469);
        double r896473 = r896471 + r896472;
        double r896474 = r896467 * r896473;
        return r896474;
}
↓
double f(double re, double im) {
        double r896475 = re;
        double r896476 = sin(r896475);
        double r896477 = im;
        double r896478 = exp(r896477);
        double r896479 = r896476 * r896478;
        double r896480 = r896476 / r896478;
        double r896481 = r896479 + r896480;
        double r896482 = 0.5;
        double r896483 = r896481 * r896482;
        return r896483;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))