Average Error: 0.0 → 0.0
Time: 3.0s
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 r41783 = 0.5;
        double r41784 = re;
        double r41785 = cos(r41784);
        double r41786 = r41783 * r41785;
        double r41787 = im;
        double r41788 = -r41787;
        double r41789 = exp(r41788);
        double r41790 = exp(r41787);
        double r41791 = r41789 + r41790;
        double r41792 = r41786 * r41791;
        return r41792;
}
↓
double f(double re, double im) {
        double r41793 = 0.5;
        double r41794 = re;
        double r41795 = cos(r41794);
        double r41796 = r41793 * r41795;
        double r41797 = im;
        double r41798 = -r41797;
        double r41799 = exp(r41798);
        double r41800 = exp(r41797);
        double r41801 = r41799 + r41800;
        double r41802 = r41796 * r41801;
        return r41802;
}

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 2020002 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))