Average Error: 0.0 → 0.0
Time: 44.8s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(\frac{\cos re}{\sqrt{e^{im}}} \cdot \frac{1}{\sqrt{e^{im}}} + e^{im} \cdot \cos re\right) \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(\frac{\cos re}{\sqrt{e^{im}}} \cdot \frac{1}{\sqrt{e^{im}}} + e^{im} \cdot \cos re\right) \cdot 0.5
double f(double re, double im) {
        double r1466266 = 0.5;
        double r1466267 = re;
        double r1466268 = cos(r1466267);
        double r1466269 = r1466266 * r1466268;
        double r1466270 = im;
        double r1466271 = -r1466270;
        double r1466272 = exp(r1466271);
        double r1466273 = exp(r1466270);
        double r1466274 = r1466272 + r1466273;
        double r1466275 = r1466269 * r1466274;
        return r1466275;
}
↓
double f(double re, double im) {
        double r1466276 = re;
        double r1466277 = cos(r1466276);
        double r1466278 = im;
        double r1466279 = exp(r1466278);
        double r1466280 = sqrt(r1466279);
        double r1466281 = r1466277 / r1466280;
        double r1466282 = 1.0;
        double r1466283 = r1466282 / r1466280;
        double r1466284 = r1466281 * r1466283;
        double r1466285 = r1466279 * r1466277;
        double r1466286 = r1466284 + r1466285;
        double r1466287 = 0.5;
        double r1466288 = r1466286 * r1466287;
        return r1466288;
}

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 add-sqr-sqrt0.0

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

  5. Applied *-un-lft-identity0.0

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

  6. Applied times-frac0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019149 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))