Average Error: 0.0 → 0.0
Time: 16.3s
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 r1667785 = 0.5;
        double r1667786 = re;
        double r1667787 = cos(r1667786);
        double r1667788 = r1667785 * r1667787;
        double r1667789 = im;
        double r1667790 = -r1667789;
        double r1667791 = exp(r1667790);
        double r1667792 = exp(r1667789);
        double r1667793 = r1667791 + r1667792;
        double r1667794 = r1667788 * r1667793;
        return r1667794;
}
↓
double f(double re, double im) {
        double r1667795 = im;
        double r1667796 = exp(r1667795);
        double r1667797 = -r1667795;
        double r1667798 = exp(r1667797);
        double r1667799 = r1667796 + r1667798;
        double r1667800 = 0.5;
        double r1667801 = re;
        double r1667802 = cos(r1667801);
        double r1667803 = r1667800 * r1667802;
        double r1667804 = r1667799 * r1667803;
        return r1667804;
}

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