Average Error: 0.0 → 0.0
Time: 29.5s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[0.5 \cdot \left(\left(\frac{1}{e^{im}} + e^{im}\right) \cdot \cos re\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
0.5 \cdot \left(\left(\frac{1}{e^{im}} + e^{im}\right) \cdot \cos re\right)
double f(double re, double im) {
        double r2019243 = 0.5;
        double r2019244 = re;
        double r2019245 = cos(r2019244);
        double r2019246 = r2019243 * r2019245;
        double r2019247 = im;
        double r2019248 = -r2019247;
        double r2019249 = exp(r2019248);
        double r2019250 = exp(r2019247);
        double r2019251 = r2019249 + r2019250;
        double r2019252 = r2019246 * r2019251;
        return r2019252;
}
↓
double f(double re, double im) {
        double r2019253 = 0.5;
        double r2019254 = 1.0;
        double r2019255 = im;
        double r2019256 = exp(r2019255);
        double r2019257 = r2019254 / r2019256;
        double r2019258 = r2019257 + r2019256;
        double r2019259 = re;
        double r2019260 = cos(r2019259);
        double r2019261 = r2019258 * r2019260;
        double r2019262 = r2019253 * r2019261;
        return r2019262;
}

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. Using strategy rm

  4. Applied div-inv0.0

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

  5. Applied distribute-lft-out0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019143 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))