Average Error: 0.0 → 0.0
Time: 37.7s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(e^{\log \left(\sqrt{0.5} \cdot \frac{\sqrt{0.5}}{e^{im}}\right)} + e^{im} \cdot 0.5\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(e^{\log \left(\sqrt{0.5} \cdot \frac{\sqrt{0.5}}{e^{im}}\right)} + e^{im} \cdot 0.5\right)
double f(double re, double im) {
        double r2475168 = 0.5;
        double r2475169 = re;
        double r2475170 = cos(r2475169);
        double r2475171 = r2475168 * r2475170;
        double r2475172 = im;
        double r2475173 = -r2475172;
        double r2475174 = exp(r2475173);
        double r2475175 = exp(r2475172);
        double r2475176 = r2475174 + r2475175;
        double r2475177 = r2475171 * r2475176;
        return r2475177;
}
↓
double f(double re, double im) {
        double r2475178 = re;
        double r2475179 = cos(r2475178);
        double r2475180 = 0.5;
        double r2475181 = sqrt(r2475180);
        double r2475182 = im;
        double r2475183 = exp(r2475182);
        double r2475184 = r2475181 / r2475183;
        double r2475185 = r2475181 * r2475184;
        double r2475186 = log(r2475185);
        double r2475187 = exp(r2475186);
        double r2475188 = r2475183 * r2475180;
        double r2475189 = r2475187 + r2475188;
        double r2475190 = r2475179 * r2475189;
        return r2475190;
}

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 *-un-lft-identity0.0

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

  5. Applied add-sqr-sqrt0.0

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

  6. Applied times-frac0.0

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

  7. Simplified0.0

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

  9. Applied add-exp-log0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019104 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))