Average Error: 0.0 → 0.0
Time: 24.8s
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 r42983 = 0.5;
        double r42984 = re;
        double r42985 = cos(r42984);
        double r42986 = r42983 * r42985;
        double r42987 = im;
        double r42988 = -r42987;
        double r42989 = exp(r42988);
        double r42990 = exp(r42987);
        double r42991 = r42989 + r42990;
        double r42992 = r42986 * r42991;
        return r42992;
}
↓
double f(double re, double im) {
        double r42993 = 0.5;
        double r42994 = re;
        double r42995 = cos(r42994);
        double r42996 = r42993 * r42995;
        double r42997 = im;
        double r42998 = -r42997;
        double r42999 = exp(r42998);
        double r43000 = exp(r42997);
        double r43001 = r42999 + r43000;
        double r43002 = r42996 * r43001;
        return r43002;
}

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 2019323 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))