Average Error: 0.0 → 0.0
Time: 19.5s
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 r943541 = 0.5;
        double r943542 = re;
        double r943543 = cos(r943542);
        double r943544 = r943541 * r943543;
        double r943545 = im;
        double r943546 = -r943545;
        double r943547 = exp(r943546);
        double r943548 = exp(r943545);
        double r943549 = r943547 + r943548;
        double r943550 = r943544 * r943549;
        return r943550;
}
↓
double f(double re, double im) {
        double r943551 = re;
        double r943552 = cos(r943551);
        double r943553 = 0.5;
        double r943554 = im;
        double r943555 = exp(r943554);
        double r943556 = r943553 / r943555;
        double r943557 = r943553 * r943555;
        double r943558 = r943556 + r943557;
        double r943559 = r943552 * r943558;
        return r943559;
}

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 2019137 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))