Average Error: 0.0 → 0.0
Time: 11.1s
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 r42183 = 0.5;
        double r42184 = re;
        double r42185 = cos(r42184);
        double r42186 = r42183 * r42185;
        double r42187 = im;
        double r42188 = -r42187;
        double r42189 = exp(r42188);
        double r42190 = exp(r42187);
        double r42191 = r42189 + r42190;
        double r42192 = r42186 * r42191;
        return r42192;
}
↓
double f(double re, double im) {
        double r42193 = 0.5;
        double r42194 = re;
        double r42195 = cos(r42194);
        double r42196 = r42193 * r42195;
        double r42197 = im;
        double r42198 = -r42197;
        double r42199 = exp(r42198);
        double r42200 = exp(r42197);
        double r42201 = r42199 + r42200;
        double r42202 = r42196 * r42201;
        return r42202;
}

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 2019326 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))