Average Error: 0.0 → 0.0
Time: 4.2s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}
double f(double re, double im) {
        double r90509 = 0.5;
        double r90510 = re;
        double r90511 = cos(r90510);
        double r90512 = r90509 * r90511;
        double r90513 = im;
        double r90514 = -r90513;
        double r90515 = exp(r90514);
        double r90516 = exp(r90513);
        double r90517 = r90515 + r90516;
        double r90518 = r90512 * r90517;
        return r90518;
}
↓
double f(double re, double im) {
        double r90519 = 0.5;
        double r90520 = re;
        double r90521 = cos(r90520);
        double r90522 = r90519 * r90521;
        double r90523 = im;
        double r90524 = exp(r90523);
        double r90525 = r90522 / r90524;
        double r90526 = r90522 * r90524;
        double r90527 = r90525 + r90526;
        return r90527;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))