Average Error: 0.0 → 0.0
Time: 3.4s
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 r101441 = 0.5;
        double r101442 = re;
        double r101443 = cos(r101442);
        double r101444 = r101441 * r101443;
        double r101445 = im;
        double r101446 = -r101445;
        double r101447 = exp(r101446);
        double r101448 = exp(r101445);
        double r101449 = r101447 + r101448;
        double r101450 = r101444 * r101449;
        return r101450;
}
↓
double f(double re, double im) {
        double r101451 = 0.5;
        double r101452 = re;
        double r101453 = cos(r101452);
        double r101454 = r101451 * r101453;
        double r101455 = im;
        double r101456 = exp(r101455);
        double r101457 = r101454 / r101456;
        double r101458 = r101454 * r101456;
        double r101459 = r101457 + r101458;
        return r101459;
}

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 2020057 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))