Average Error: 0.0 → 0.0
Time: 4.3s
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 r33889 = 0.5;
        double r33890 = re;
        double r33891 = cos(r33890);
        double r33892 = r33889 * r33891;
        double r33893 = im;
        double r33894 = -r33893;
        double r33895 = exp(r33894);
        double r33896 = exp(r33893);
        double r33897 = r33895 + r33896;
        double r33898 = r33892 * r33897;
        return r33898;
}
↓
double f(double re, double im) {
        double r33899 = 0.5;
        double r33900 = re;
        double r33901 = cos(r33900);
        double r33902 = r33899 * r33901;
        double r33903 = im;
        double r33904 = -r33903;
        double r33905 = exp(r33904);
        double r33906 = exp(r33903);
        double r33907 = r33905 + r33906;
        double r33908 = r33902 * r33907;
        return r33908;
}

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 2020062 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))