Average Error: 0.0 → 0.0
Time: 15.0s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)
double f(double re, double im) {
        double r43400 = 0.5;
        double r43401 = re;
        double r43402 = cos(r43401);
        double r43403 = r43400 * r43402;
        double r43404 = im;
        double r43405 = -r43404;
        double r43406 = exp(r43405);
        double r43407 = exp(r43404);
        double r43408 = r43406 + r43407;
        double r43409 = r43403 * r43408;
        return r43409;
}
↓
double f(double re, double im) {
        double r43410 = im;
        double r43411 = exp(r43410);
        double r43412 = -r43410;
        double r43413 = exp(r43412);
        double r43414 = r43411 + r43413;
        double r43415 = 0.5;
        double r43416 = re;
        double r43417 = cos(r43416);
        double r43418 = r43415 * r43417;
        double r43419 = r43414 * r43418;
        return r43419;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))