Average Error: 0.0 → 0.0
Time: 10.2s
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 r834805 = 0.5;
        double r834806 = re;
        double r834807 = cos(r834806);
        double r834808 = r834805 * r834807;
        double r834809 = im;
        double r834810 = -r834809;
        double r834811 = exp(r834810);
        double r834812 = exp(r834809);
        double r834813 = r834811 + r834812;
        double r834814 = r834808 * r834813;
        return r834814;
}
↓
double f(double re, double im) {
        double r834815 = im;
        double r834816 = exp(r834815);
        double r834817 = -r834815;
        double r834818 = exp(r834817);
        double r834819 = r834816 + r834818;
        double r834820 = 0.5;
        double r834821 = re;
        double r834822 = cos(r834821);
        double r834823 = r834820 * r834822;
        double r834824 = r834819 * r834823;
        return r834824;
}

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

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

Reproduce

herbie shell --seed 2019156 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))