Average Error: 0.0 → 0.0
Time: 14.6s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot e^{im} + \frac{\cos re}{e^{im}} \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot e^{im} + \frac{\cos re}{e^{im}} \cdot 0.5
double f(double re, double im) {
        double r27251 = 0.5;
        double r27252 = re;
        double r27253 = cos(r27252);
        double r27254 = r27251 * r27253;
        double r27255 = im;
        double r27256 = -r27255;
        double r27257 = exp(r27256);
        double r27258 = exp(r27255);
        double r27259 = r27257 + r27258;
        double r27260 = r27254 * r27259;
        return r27260;
}
↓
double f(double re, double im) {
        double r27261 = 0.5;
        double r27262 = re;
        double r27263 = cos(r27262);
        double r27264 = r27261 * r27263;
        double r27265 = im;
        double r27266 = exp(r27265);
        double r27267 = r27264 * r27266;
        double r27268 = r27263 / r27266;
        double r27269 = r27268 * r27261;
        double r27270 = r27267 + r27269;
        return r27270;
}

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

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))