Average Error: 0.0 → 0.0
Time: 3.6s
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 r47572 = 0.5;
        double r47573 = re;
        double r47574 = cos(r47573);
        double r47575 = r47572 * r47574;
        double r47576 = im;
        double r47577 = -r47576;
        double r47578 = exp(r47577);
        double r47579 = exp(r47576);
        double r47580 = r47578 + r47579;
        double r47581 = r47575 * r47580;
        return r47581;
}
↓
double f(double re, double im) {
        double r47582 = 0.5;
        double r47583 = re;
        double r47584 = cos(r47583);
        double r47585 = r47582 * r47584;
        double r47586 = im;
        double r47587 = exp(r47586);
        double r47588 = r47585 / r47587;
        double r47589 = r47585 * r47587;
        double r47590 = r47588 + r47589;
        return r47590;
}

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 2020001 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))