Average Error: 0.0 → 0.0
Time: 10.4s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right)
double f(double re, double im) {
        double r739049 = 0.5;
        double r739050 = re;
        double r739051 = cos(r739050);
        double r739052 = r739049 * r739051;
        double r739053 = im;
        double r739054 = -r739053;
        double r739055 = exp(r739054);
        double r739056 = exp(r739053);
        double r739057 = r739055 + r739056;
        double r739058 = r739052 * r739057;
        return r739058;
}
↓
double f(double re, double im) {
        double r739059 = re;
        double r739060 = cos(r739059);
        double r739061 = 0.5;
        double r739062 = im;
        double r739063 = exp(r739062);
        double r739064 = r739061 / r739063;
        double r739065 = r739063 * r739061;
        double r739066 = r739064 + r739065;
        double r739067 = r739060 * r739066;
        return r739067;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019151 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))