Average Error: 0.0 → 0.0
Time: 4.6s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}
double f(double re, double im) {
        double r47887 = 0.5;
        double r47888 = re;
        double r47889 = cos(r47888);
        double r47890 = r47887 * r47889;
        double r47891 = im;
        double r47892 = -r47891;
        double r47893 = exp(r47892);
        double r47894 = exp(r47891);
        double r47895 = r47893 + r47894;
        double r47896 = r47890 * r47895;
        return r47896;
}
↓
double f(double re, double im) {
        double r47897 = 0.5;
        double r47898 = re;
        double r47899 = cos(r47898);
        double r47900 = r47897 * r47899;
        double r47901 = im;
        double r47902 = exp(r47901);
        double r47903 = r47900 / r47902;
        double r47904 = r47900 * r47902;
        double r47905 = r47903 + r47904;
        return r47905;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))