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 r43671 = 0.5;
        double r43672 = re;
        double r43673 = cos(r43672);
        double r43674 = r43671 * r43673;
        double r43675 = im;
        double r43676 = -r43675;
        double r43677 = exp(r43676);
        double r43678 = exp(r43675);
        double r43679 = r43677 + r43678;
        double r43680 = r43674 * r43679;
        return r43680;
}
↓
double f(double re, double im) {
        double r43681 = 0.5;
        double r43682 = re;
        double r43683 = cos(r43682);
        double r43684 = r43681 * r43683;
        double r43685 = im;
        double r43686 = exp(r43685);
        double r43687 = r43684 / r43686;
        double r43688 = r43684 * r43686;
        double r43689 = r43687 + r43688;
        return r43689;
}

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 2020020 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))