Average Error: 0.0 → 0.0
Time: 23.2s
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 r43897 = 0.5;
        double r43898 = re;
        double r43899 = cos(r43898);
        double r43900 = r43897 * r43899;
        double r43901 = im;
        double r43902 = -r43901;
        double r43903 = exp(r43902);
        double r43904 = exp(r43901);
        double r43905 = r43903 + r43904;
        double r43906 = r43900 * r43905;
        return r43906;
}
↓
double f(double re, double im) {
        double r43907 = 0.5;
        double r43908 = re;
        double r43909 = cos(r43908);
        double r43910 = r43907 * r43909;
        double r43911 = im;
        double r43912 = -r43911;
        double r43913 = exp(r43912);
        double r43914 = exp(r43911);
        double r43915 = r43913 + r43914;
        double r43916 = r43910 * r43915;
        return r43916;
}

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 2019323 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))