Average Error: 0.0 → 0.0
Time: 14.7s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(e^{im} \cdot 0.5\right) + \frac{0.5}{e^{im}} \cdot \cos re\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(e^{im} \cdot 0.5\right) + \frac{0.5}{e^{im}} \cdot \cos re
double f(double re, double im) {
        double r861687 = 0.5;
        double r861688 = re;
        double r861689 = cos(r861688);
        double r861690 = r861687 * r861689;
        double r861691 = im;
        double r861692 = -r861691;
        double r861693 = exp(r861692);
        double r861694 = exp(r861691);
        double r861695 = r861693 + r861694;
        double r861696 = r861690 * r861695;
        return r861696;
}
↓
double f(double re, double im) {
        double r861697 = re;
        double r861698 = cos(r861697);
        double r861699 = im;
        double r861700 = exp(r861699);
        double r861701 = 0.5;
        double r861702 = r861700 * r861701;
        double r861703 = r861698 * r861702;
        double r861704 = r861701 / r861700;
        double r861705 = r861704 * r861698;
        double r861706 = r861703 + r861705;
        return r861706;
}

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. Simplified0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))