Average Error: 0.0 → 0.0
Time: 14.3s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(\cos re \cdot e^{im} + \frac{\cos re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(\cos re \cdot e^{im} + \frac{\cos re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r1377555 = 0.5;
        double r1377556 = re;
        double r1377557 = cos(r1377556);
        double r1377558 = r1377555 * r1377557;
        double r1377559 = im;
        double r1377560 = -r1377559;
        double r1377561 = exp(r1377560);
        double r1377562 = exp(r1377559);
        double r1377563 = r1377561 + r1377562;
        double r1377564 = r1377558 * r1377563;
        return r1377564;
}
↓
double f(double re, double im) {
        double r1377565 = re;
        double r1377566 = cos(r1377565);
        double r1377567 = im;
        double r1377568 = exp(r1377567);
        double r1377569 = r1377566 * r1377568;
        double r1377570 = r1377566 / r1377568;
        double r1377571 = r1377569 + r1377570;
        double r1377572 = 0.5;
        double r1377573 = r1377571 * r1377572;
        return r1377573;
}

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. Taylor expanded around -inf 0.0

    \[\leadsto \color{blue}{0.5 \cdot \left(\left(e^{im} + e^{-1 \cdot im}\right) \cdot \cos re\right)}\]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019129 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))