Average Error: 0.0 → 0.0
Time: 13.1s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[e^{im} \cdot \left(0.5 \cdot \cos re\right) + \frac{\cos re}{e^{im}} \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
e^{im} \cdot \left(0.5 \cdot \cos re\right) + \frac{\cos re}{e^{im}} \cdot 0.5
double f(double re, double im) {
        double r31481 = 0.5;
        double r31482 = re;
        double r31483 = cos(r31482);
        double r31484 = r31481 * r31483;
        double r31485 = im;
        double r31486 = -r31485;
        double r31487 = exp(r31486);
        double r31488 = exp(r31485);
        double r31489 = r31487 + r31488;
        double r31490 = r31484 * r31489;
        return r31490;
}
↓
double f(double re, double im) {
        double r31491 = im;
        double r31492 = exp(r31491);
        double r31493 = 0.5;
        double r31494 = re;
        double r31495 = cos(r31494);
        double r31496 = r31493 * r31495;
        double r31497 = r31492 * r31496;
        double r31498 = r31495 / r31492;
        double r31499 = r31498 * r31493;
        double r31500 = r31497 + r31499;
        return r31500;
}

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

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))