Average Error: 0.0 → 0.0
Time: 19.6s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)
double f(double re, double im) {
        double r792552 = 0.5;
        double r792553 = re;
        double r792554 = cos(r792553);
        double r792555 = r792552 * r792554;
        double r792556 = im;
        double r792557 = -r792556;
        double r792558 = exp(r792557);
        double r792559 = exp(r792556);
        double r792560 = r792558 + r792559;
        double r792561 = r792555 * r792560;
        return r792561;
}
↓
double f(double re, double im) {
        double r792562 = re;
        double r792563 = cos(r792562);
        double r792564 = im;
        double r792565 = exp(r792564);
        double r792566 = 0.5;
        double r792567 = r792565 * r792566;
        double r792568 = r792566 / r792565;
        double r792569 = r792567 + r792568;
        double r792570 = r792563 * r792569;
        return r792570;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019139 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))