Average Error: 0.0 → 0.0
Time: 22.4s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - 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 r540452 = 0.5;
        double r540453 = re;
        double r540454 = sin(r540453);
        double r540455 = r540452 * r540454;
        double r540456 = 0.0;
        double r540457 = im;
        double r540458 = r540456 - r540457;
        double r540459 = exp(r540458);
        double r540460 = exp(r540457);
        double r540461 = r540459 + r540460;
        double r540462 = r540455 * r540461;
        return r540462;
}
↓
double f(double re, double im) {
        double r540463 = im;
        double r540464 = exp(r540463);
        double r540465 = re;
        double r540466 = sin(r540465);
        double r540467 = r540464 * r540466;
        double r540468 = r540466 / r540464;
        double r540469 = r540467 + r540468;
        double r540470 = 0.5;
        double r540471 = r540469 * r540470;
        return r540471;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019132 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))