Average Error: 0.0 → 0.0
Time: 1.7m
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(\frac{\sin re}{e^{im}} + e^{im} \cdot \sin re\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(\frac{\sin re}{e^{im}} + e^{im} \cdot \sin re\right) \cdot 0.5
double f(double re, double im) {
        double r1177360 = 0.5;
        double r1177361 = re;
        double r1177362 = sin(r1177361);
        double r1177363 = r1177360 * r1177362;
        double r1177364 = 0.0;
        double r1177365 = im;
        double r1177366 = r1177364 - r1177365;
        double r1177367 = exp(r1177366);
        double r1177368 = exp(r1177365);
        double r1177369 = r1177367 + r1177368;
        double r1177370 = r1177363 * r1177369;
        return r1177370;
}
↓
double f(double re, double im) {
        double r1177371 = re;
        double r1177372 = sin(r1177371);
        double r1177373 = im;
        double r1177374 = exp(r1177373);
        double r1177375 = r1177372 / r1177374;
        double r1177376 = r1177374 * r1177372;
        double r1177377 = r1177375 + r1177376;
        double r1177378 = 0.5;
        double r1177379 = r1177377 * r1177378;
        return r1177379;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))