Average Error: 0.0 → 0.0
Time: 13.4s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot e^{im} + \frac{0.5}{e^{im}} \cdot \cos re\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot e^{im} + \frac{0.5}{e^{im}} \cdot \cos re
double f(double re, double im) {
        double r36357 = 0.5;
        double r36358 = re;
        double r36359 = cos(r36358);
        double r36360 = r36357 * r36359;
        double r36361 = im;
        double r36362 = -r36361;
        double r36363 = exp(r36362);
        double r36364 = exp(r36361);
        double r36365 = r36363 + r36364;
        double r36366 = r36360 * r36365;
        return r36366;
}
↓
double f(double re, double im) {
        double r36367 = 0.5;
        double r36368 = re;
        double r36369 = cos(r36368);
        double r36370 = r36367 * r36369;
        double r36371 = im;
        double r36372 = exp(r36371);
        double r36373 = r36370 * r36372;
        double r36374 = r36367 / r36372;
        double r36375 = r36374 * r36369;
        double r36376 = r36373 + r36375;
        return r36376;
}

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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))