Average Error: 0.0 → 0.0
Time: 13.4s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)
double f(double re, double im) {
        double r1803735 = 0.5;
        double r1803736 = re;
        double r1803737 = cos(r1803736);
        double r1803738 = r1803735 * r1803737;
        double r1803739 = im;
        double r1803740 = -r1803739;
        double r1803741 = exp(r1803740);
        double r1803742 = exp(r1803739);
        double r1803743 = r1803741 + r1803742;
        double r1803744 = r1803738 * r1803743;
        return r1803744;
}
↓
double f(double re, double im) {
        double r1803745 = re;
        double r1803746 = cos(r1803745);
        double r1803747 = 0.5;
        double r1803748 = im;
        double r1803749 = exp(r1803748);
        double r1803750 = r1803747 / r1803749;
        double r1803751 = r1803747 * r1803749;
        double r1803752 = r1803750 + r1803751;
        double r1803753 = r1803746 * r1803752;
        return r1803753;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))