Average Error: 0.0 → 0.0
Time: 13.9s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(\sqrt{0.5} \cdot \frac{\sqrt{0.5}}{e^{im}} + 0.5 \cdot e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(\sqrt{0.5} \cdot \frac{\sqrt{0.5}}{e^{im}} + 0.5 \cdot e^{im}\right)
double f(double re, double im) {
        double r1252509 = 0.5;
        double r1252510 = re;
        double r1252511 = cos(r1252510);
        double r1252512 = r1252509 * r1252511;
        double r1252513 = im;
        double r1252514 = -r1252513;
        double r1252515 = exp(r1252514);
        double r1252516 = exp(r1252513);
        double r1252517 = r1252515 + r1252516;
        double r1252518 = r1252512 * r1252517;
        return r1252518;
}
↓
double f(double re, double im) {
        double r1252519 = re;
        double r1252520 = cos(r1252519);
        double r1252521 = 0.5;
        double r1252522 = sqrt(r1252521);
        double r1252523 = im;
        double r1252524 = exp(r1252523);
        double r1252525 = r1252522 / r1252524;
        double r1252526 = r1252522 * r1252525;
        double r1252527 = r1252521 * r1252524;
        double r1252528 = r1252526 + r1252527;
        double r1252529 = r1252520 * r1252528;
        return r1252529;
}

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

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

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

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

  5. Applied add-sqr-sqrt0.0

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

  6. Applied times-frac0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019154 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))