Average Error: 0.0 → 0.0
Time: 13.1s
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 r964639 = 0.5;
        double r964640 = re;
        double r964641 = cos(r964640);
        double r964642 = r964639 * r964641;
        double r964643 = im;
        double r964644 = -r964643;
        double r964645 = exp(r964644);
        double r964646 = exp(r964643);
        double r964647 = r964645 + r964646;
        double r964648 = r964642 * r964647;
        return r964648;
}
↓
double f(double re, double im) {
        double r964649 = re;
        double r964650 = cos(r964649);
        double r964651 = 0.5;
        double r964652 = im;
        double r964653 = exp(r964652);
        double r964654 = r964651 / r964653;
        double r964655 = r964653 * r964651;
        double r964656 = r964654 + r964655;
        double r964657 = r964650 * r964656;
        return r964657;
}

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 2019155 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))