Average Error: 0.0 → 0.0
Time: 19.0s
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 r49307 = 0.5;
        double r49308 = re;
        double r49309 = cos(r49308);
        double r49310 = r49307 * r49309;
        double r49311 = im;
        double r49312 = -r49311;
        double r49313 = exp(r49312);
        double r49314 = exp(r49311);
        double r49315 = r49313 + r49314;
        double r49316 = r49310 * r49315;
        return r49316;
}
↓
double f(double re, double im) {
        double r49317 = 0.5;
        double r49318 = re;
        double r49319 = cos(r49318);
        double r49320 = r49317 * r49319;
        double r49321 = im;
        double r49322 = -r49321;
        double r49323 = exp(r49322);
        double r49324 = exp(r49321);
        double r49325 = r49323 + r49324;
        double r49326 = r49320 * r49325;
        return r49326;
}

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 2019325 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))