Average Error: 0.0 → 0.0
Time: 3.7s
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 r47253 = 0.5;
        double r47254 = re;
        double r47255 = cos(r47254);
        double r47256 = r47253 * r47255;
        double r47257 = im;
        double r47258 = -r47257;
        double r47259 = exp(r47258);
        double r47260 = exp(r47257);
        double r47261 = r47259 + r47260;
        double r47262 = r47256 * r47261;
        return r47262;
}
↓
double f(double re, double im) {
        double r47263 = 0.5;
        double r47264 = re;
        double r47265 = cos(r47264);
        double r47266 = r47263 * r47265;
        double r47267 = im;
        double r47268 = exp(r47267);
        double r47269 = r47266 / r47268;
        double r47270 = r47266 * r47268;
        double r47271 = r47269 + r47270;
        return r47271;
}

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 2020001 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))