Average Error: 0.0 → 0.0
Time: 22.8s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} \cdot \cos re + \frac{\cos re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} \cdot \cos re + \frac{\cos re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r2406277 = 0.5;
        double r2406278 = re;
        double r2406279 = cos(r2406278);
        double r2406280 = r2406277 * r2406279;
        double r2406281 = im;
        double r2406282 = -r2406281;
        double r2406283 = exp(r2406282);
        double r2406284 = exp(r2406281);
        double r2406285 = r2406283 + r2406284;
        double r2406286 = r2406280 * r2406285;
        return r2406286;
}
↓
double f(double re, double im) {
        double r2406287 = im;
        double r2406288 = exp(r2406287);
        double r2406289 = re;
        double r2406290 = cos(r2406289);
        double r2406291 = r2406288 * r2406290;
        double r2406292 = r2406290 / r2406288;
        double r2406293 = r2406291 + r2406292;
        double r2406294 = 0.5;
        double r2406295 = r2406293 * r2406294;
        return r2406295;
}

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

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))