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 r258282 = 0.5;
        double r258283 = re;
        double r258284 = sin(r258283);
        double r258285 = r258282 * r258284;
        double r258286 = 0.0;
        double r258287 = im;
        double r258288 = r258286 - r258287;
        double r258289 = exp(r258288);
        double r258290 = exp(r258287);
        double r258291 = r258289 + r258290;
        double r258292 = r258285 * r258291;
        return r258292;
}
↓
double f(double re, double im) {
        double r258293 = im;
        double r258294 = exp(r258293);
        double r258295 = re;
        double r258296 = sin(r258295);
        double r258297 = r258294 * r258296;
        double r258298 = r258296 / r258294;
        double r258299 = r258297 + r258298;
        double r258300 = 0.5;
        double r258301 = r258299 * r258300;
        return r258301;
}

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 2019139 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))