Average Error: 0.0 → 0.0
Time: 19.3s
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 r1155146 = 0.5;
        double r1155147 = re;
        double r1155148 = cos(r1155147);
        double r1155149 = r1155146 * r1155148;
        double r1155150 = im;
        double r1155151 = -r1155150;
        double r1155152 = exp(r1155151);
        double r1155153 = exp(r1155150);
        double r1155154 = r1155152 + r1155153;
        double r1155155 = r1155149 * r1155154;
        return r1155155;
}
↓
double f(double re, double im) {
        double r1155156 = im;
        double r1155157 = exp(r1155156);
        double r1155158 = -r1155156;
        double r1155159 = exp(r1155158);
        double r1155160 = r1155157 + r1155159;
        double r1155161 = 0.5;
        double r1155162 = re;
        double r1155163 = cos(r1155162);
        double r1155164 = r1155161 * r1155163;
        double r1155165 = r1155160 * r1155164;
        return r1155165;
}

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 2019152 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))