Average Error: 0.0 → 0.0
Time: 15.1s
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 r4316328 = 0.5;
        double r4316329 = re;
        double r4316330 = cos(r4316329);
        double r4316331 = r4316328 * r4316330;
        double r4316332 = im;
        double r4316333 = -r4316332;
        double r4316334 = exp(r4316333);
        double r4316335 = exp(r4316332);
        double r4316336 = r4316334 + r4316335;
        double r4316337 = r4316331 * r4316336;
        return r4316337;
}
↓
double f(double re, double im) {
        double r4316338 = 0.5;
        double r4316339 = re;
        double r4316340 = cos(r4316339);
        double r4316341 = r4316338 * r4316340;
        double r4316342 = im;
        double r4316343 = -r4316342;
        double r4316344 = exp(r4316343);
        double r4316345 = exp(r4316342);
        double r4316346 = r4316344 + r4316345;
        double r4316347 = r4316341 * r4316346;
        return r4316347;
}

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