Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r45354 = 0.5;
        double r45355 = re;
        double r45356 = cos(r45355);
        double r45357 = r45354 * r45356;
        double r45358 = im;
        double r45359 = -r45358;
        double r45360 = exp(r45359);
        double r45361 = exp(r45358);
        double r45362 = r45360 + r45361;
        double r45363 = r45357 * r45362;
        return r45363;
}
↓
double f(double re, double im) {
        double r45364 = 0.5;
        double r45365 = re;
        double r45366 = cos(r45365);
        double r45367 = r45364 * r45366;
        double r45368 = im;
        double r45369 = -r45368;
        double r45370 = exp(r45369);
        double r45371 = exp(r45368);
        double r45372 = r45370 + r45371;
        double r45373 = r45367 * r45372;
        return r45373;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))