Average Error: 0.0 → 0.0
Time: 1.3m
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)
double f(double re, double im) {
        double r2714031 = 0.5;
        double r2714032 = re;
        double r2714033 = cos(r2714032);
        double r2714034 = r2714031 * r2714033;
        double r2714035 = im;
        double r2714036 = -r2714035;
        double r2714037 = exp(r2714036);
        double r2714038 = exp(r2714035);
        double r2714039 = r2714037 + r2714038;
        double r2714040 = r2714034 * r2714039;
        return r2714040;
}
↓
double f(double re, double im) {
        double r2714041 = im;
        double r2714042 = exp(r2714041);
        double r2714043 = -r2714041;
        double r2714044 = exp(r2714043);
        double r2714045 = r2714042 + r2714044;
        double r2714046 = 0.5;
        double r2714047 = re;
        double r2714048 = cos(r2714047);
        double r2714049 = r2714046 * r2714048;
        double r2714050 = r2714045 * r2714049;
        return r2714050;
}

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

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

Reproduce

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