Average Error: 0.0 → 0.0
Time: 18.6s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r53328 = 0.5;
        double r53329 = re;
        double r53330 = cos(r53329);
        double r53331 = r53328 * r53330;
        double r53332 = im;
        double r53333 = -r53332;
        double r53334 = exp(r53333);
        double r53335 = exp(r53332);
        double r53336 = r53334 + r53335;
        double r53337 = r53331 * r53336;
        return r53337;
}
↓
double f(double re, double im) {
        double r53338 = 0.5;
        double r53339 = re;
        double r53340 = cos(r53339);
        double r53341 = r53338 * r53340;
        double r53342 = im;
        double r53343 = -r53342;
        double r53344 = exp(r53343);
        double r53345 = exp(r53342);
        double r53346 = r53344 + r53345;
        double r53347 = r53341 * r53346;
        return r53347;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))