Average Error: 0.0 → 0.0
Time: 15.4s
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 r49963 = 0.5;
        double r49964 = re;
        double r49965 = cos(r49964);
        double r49966 = r49963 * r49965;
        double r49967 = im;
        double r49968 = -r49967;
        double r49969 = exp(r49968);
        double r49970 = exp(r49967);
        double r49971 = r49969 + r49970;
        double r49972 = r49966 * r49971;
        return r49972;
}
↓
double f(double re, double im) {
        double r49973 = im;
        double r49974 = exp(r49973);
        double r49975 = -r49973;
        double r49976 = exp(r49975);
        double r49977 = r49974 + r49976;
        double r49978 = 0.5;
        double r49979 = re;
        double r49980 = cos(r49979);
        double r49981 = r49978 * r49980;
        double r49982 = r49977 * r49981;
        return r49982;
}

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