Average Error: 0.0 → 0.0
Time: 15.3s
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 r862503 = 0.5;
        double r862504 = re;
        double r862505 = sin(r862504);
        double r862506 = r862503 * r862505;
        double r862507 = 0.0;
        double r862508 = im;
        double r862509 = r862507 - r862508;
        double r862510 = exp(r862509);
        double r862511 = exp(r862508);
        double r862512 = r862510 + r862511;
        double r862513 = r862506 * r862512;
        return r862513;
}
↓
double f(double re, double im) {
        double r862514 = im;
        double r862515 = exp(r862514);
        double r862516 = re;
        double r862517 = sin(r862516);
        double r862518 = r862515 * r862517;
        double r862519 = r862517 / r862515;
        double r862520 = r862518 + r862519;
        double r862521 = 0.5;
        double r862522 = r862520 * r862521;
        return r862522;
}

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 2019172 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))