Average Error: 0.0 → 0.7
Time: 14.7s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(\frac{1}{12} \cdot {im}^{4} + \left({im}^{2} + 2\right)\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(\frac{1}{12} \cdot {im}^{4} + \left({im}^{2} + 2\right)\right)
double f(double re, double im) {
        double r32990 = 0.5;
        double r32991 = re;
        double r32992 = cos(r32991);
        double r32993 = r32990 * r32992;
        double r32994 = im;
        double r32995 = -r32994;
        double r32996 = exp(r32995);
        double r32997 = exp(r32994);
        double r32998 = r32996 + r32997;
        double r32999 = r32993 * r32998;
        return r32999;
}
↓
double f(double re, double im) {
        double r33000 = 0.5;
        double r33001 = re;
        double r33002 = cos(r33001);
        double r33003 = r33000 * r33002;
        double r33004 = 0.08333333333333333;
        double r33005 = im;
        double r33006 = 4.0;
        double r33007 = pow(r33005, r33006);
        double r33008 = r33004 * r33007;
        double r33009 = 2.0;
        double r33010 = pow(r33005, r33009);
        double r33011 = r33010 + r33009;
        double r33012 = r33008 + r33011;
        double r33013 = r33003 * r33012;
        return r33013;
}

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 0 0.7

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \color{blue}{\left(\frac{1}{12} \cdot {im}^{4} + \left({im}^{2} + 2\right)\right)}\]

  3. Final simplification0.7

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \left(\frac{1}{12} \cdot {im}^{4} + \left({im}^{2} + 2\right)\right)\]

Reproduce

herbie shell --seed 2019304 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))