Average Error: 0.0 → 0.0
Time: 6.6s
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 r55902 = 0.5;
        double r55903 = re;
        double r55904 = cos(r55903);
        double r55905 = r55902 * r55904;
        double r55906 = im;
        double r55907 = -r55906;
        double r55908 = exp(r55907);
        double r55909 = exp(r55906);
        double r55910 = r55908 + r55909;
        double r55911 = r55905 * r55910;
        return r55911;
}
↓
double f(double re, double im) {
        double r55912 = 0.5;
        double r55913 = re;
        double r55914 = cos(r55913);
        double r55915 = r55912 * r55914;
        double r55916 = im;
        double r55917 = -r55916;
        double r55918 = exp(r55917);
        double r55919 = exp(r55916);
        double r55920 = r55918 + r55919;
        double r55921 = r55915 * r55920;
        return r55921;
}

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 2019322 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))