Average Error: 0.0 → 0.0
Time: 24.5s
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 r3826307 = 0.5;
        double r3826308 = re;
        double r3826309 = cos(r3826308);
        double r3826310 = r3826307 * r3826309;
        double r3826311 = im;
        double r3826312 = -r3826311;
        double r3826313 = exp(r3826312);
        double r3826314 = exp(r3826311);
        double r3826315 = r3826313 + r3826314;
        double r3826316 = r3826310 * r3826315;
        return r3826316;
}
↓
double f(double re, double im) {
        double r3826317 = re;
        double r3826318 = cos(r3826317);
        double r3826319 = 0.5;
        double r3826320 = im;
        double r3826321 = exp(r3826320);
        double r3826322 = r3826319 / r3826321;
        double r3826323 = r3826319 * r3826321;
        double r3826324 = r3826322 + r3826323;
        double r3826325 = r3826318 * r3826324;
        return r3826325;
}

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))))