Average Error: 0.0 → 0.0
Time: 17.3s
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 r2555903 = 0.5;
        double r2555904 = re;
        double r2555905 = cos(r2555904);
        double r2555906 = r2555903 * r2555905;
        double r2555907 = im;
        double r2555908 = -r2555907;
        double r2555909 = exp(r2555908);
        double r2555910 = exp(r2555907);
        double r2555911 = r2555909 + r2555910;
        double r2555912 = r2555906 * r2555911;
        return r2555912;
}
↓
double f(double re, double im) {
        double r2555913 = im;
        double r2555914 = exp(r2555913);
        double r2555915 = -r2555913;
        double r2555916 = exp(r2555915);
        double r2555917 = r2555914 + r2555916;
        double r2555918 = 0.5;
        double r2555919 = re;
        double r2555920 = cos(r2555919);
        double r2555921 = r2555918 * r2555920;
        double r2555922 = r2555917 * r2555921;
        return r2555922;
}

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 2019171 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))