Average Error: 0.0 → 0.0
Time: 25.4s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} \cdot \cos re + \frac{\cos re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} \cdot \cos re + \frac{\cos re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r1386542 = 0.5;
        double r1386543 = re;
        double r1386544 = cos(r1386543);
        double r1386545 = r1386542 * r1386544;
        double r1386546 = im;
        double r1386547 = -r1386546;
        double r1386548 = exp(r1386547);
        double r1386549 = exp(r1386546);
        double r1386550 = r1386548 + r1386549;
        double r1386551 = r1386545 * r1386550;
        return r1386551;
}
↓
double f(double re, double im) {
        double r1386552 = im;
        double r1386553 = exp(r1386552);
        double r1386554 = re;
        double r1386555 = cos(r1386554);
        double r1386556 = r1386553 * r1386555;
        double r1386557 = r1386555 / r1386553;
        double r1386558 = r1386556 + r1386557;
        double r1386559 = 0.5;
        double r1386560 = r1386558 * r1386559;
        return r1386560;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019146 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))