Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r31850 = 0.5;
        double r31851 = re;
        double r31852 = cos(r31851);
        double r31853 = r31850 * r31852;
        double r31854 = im;
        double r31855 = -r31854;
        double r31856 = exp(r31855);
        double r31857 = exp(r31854);
        double r31858 = r31856 + r31857;
        double r31859 = r31853 * r31858;
        return r31859;
}
↓
double f(double re, double im) {
        double r31860 = 0.5;
        double r31861 = re;
        double r31862 = cos(r31861);
        double r31863 = r31860 * r31862;
        double r31864 = im;
        double r31865 = -r31864;
        double r31866 = exp(r31865);
        double r31867 = exp(r31864);
        double r31868 = r31866 + r31867;
        double r31869 = r31863 * r31868;
        return r31869;
}

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

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

Reproduce

herbie shell --seed 2020059 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))