Average Error: 0.0 → 0.0
Time: 4.7s
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 r96461 = 0.5;
        double r96462 = re;
        double r96463 = cos(r96462);
        double r96464 = r96461 * r96463;
        double r96465 = im;
        double r96466 = -r96465;
        double r96467 = exp(r96466);
        double r96468 = exp(r96465);
        double r96469 = r96467 + r96468;
        double r96470 = r96464 * r96469;
        return r96470;
}
↓
double f(double re, double im) {
        double r96471 = 0.5;
        double r96472 = re;
        double r96473 = cos(r96472);
        double r96474 = r96471 * r96473;
        double r96475 = im;
        double r96476 = exp(r96475);
        double r96477 = r96474 / r96476;
        double r96478 = r96474 * r96476;
        double r96479 = r96477 + r96478;
        return r96479;
}

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 2020033 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))