Average Error: 0.0 → 0.0
Time: 20.1s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(\frac{\cos re}{e^{im}} + e^{im} \cdot \cos re\right) \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(\frac{\cos re}{e^{im}} + e^{im} \cdot \cos re\right) \cdot 0.5
double f(double re, double im) {
        double r1330308 = 0.5;
        double r1330309 = re;
        double r1330310 = cos(r1330309);
        double r1330311 = r1330308 * r1330310;
        double r1330312 = im;
        double r1330313 = -r1330312;
        double r1330314 = exp(r1330313);
        double r1330315 = exp(r1330312);
        double r1330316 = r1330314 + r1330315;
        double r1330317 = r1330311 * r1330316;
        return r1330317;
}
↓
double f(double re, double im) {
        double r1330318 = re;
        double r1330319 = cos(r1330318);
        double r1330320 = im;
        double r1330321 = exp(r1330320);
        double r1330322 = r1330319 / r1330321;
        double r1330323 = r1330321 * r1330319;
        double r1330324 = r1330322 + r1330323;
        double r1330325 = 0.5;
        double r1330326 = r1330324 * r1330325;
        return r1330326;
}

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

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

  4. Applied add-exp-log0.0

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

  5. Applied div-exp0.0

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

  6. Taylor expanded around -inf 0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019120 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))