Average Error: 0.0 → 0.0
Time: 20.7s
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 r904364 = 0.5;
        double r904365 = re;
        double r904366 = sin(r904365);
        double r904367 = r904364 * r904366;
        double r904368 = 0.0;
        double r904369 = im;
        double r904370 = r904368 - r904369;
        double r904371 = exp(r904370);
        double r904372 = exp(r904369);
        double r904373 = r904371 + r904372;
        double r904374 = r904367 * r904373;
        return r904374;
}
↓
double f(double re, double im) {
        double r904375 = im;
        double r904376 = exp(r904375);
        double r904377 = re;
        double r904378 = sin(r904377);
        double r904379 = r904376 * r904378;
        double r904380 = r904378 / r904376;
        double r904381 = r904379 + r904380;
        double r904382 = 0.5;
        double r904383 = r904381 * r904382;
        return r904383;
}

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))))