Average Error: 0.0 → 0.0
Time: 3.7s
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 r46525 = 0.5;
        double r46526 = re;
        double r46527 = cos(r46526);
        double r46528 = r46525 * r46527;
        double r46529 = im;
        double r46530 = -r46529;
        double r46531 = exp(r46530);
        double r46532 = exp(r46529);
        double r46533 = r46531 + r46532;
        double r46534 = r46528 * r46533;
        return r46534;
}
↓
double f(double re, double im) {
        double r46535 = 0.5;
        double r46536 = re;
        double r46537 = cos(r46536);
        double r46538 = r46535 * r46537;
        double r46539 = im;
        double r46540 = exp(r46539);
        double r46541 = r46538 / r46540;
        double r46542 = r46538 * r46540;
        double r46543 = r46541 + r46542;
        return r46543;
}

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))))