Average Error: 0.0 → 0.0
Time: 17.8s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)
double f(double re, double im) {
        double r1978454 = 0.5;
        double r1978455 = re;
        double r1978456 = cos(r1978455);
        double r1978457 = r1978454 * r1978456;
        double r1978458 = im;
        double r1978459 = -r1978458;
        double r1978460 = exp(r1978459);
        double r1978461 = exp(r1978458);
        double r1978462 = r1978460 + r1978461;
        double r1978463 = r1978457 * r1978462;
        return r1978463;
}
↓
double f(double re, double im) {
        double r1978464 = re;
        double r1978465 = cos(r1978464);
        double r1978466 = 0.5;
        double r1978467 = im;
        double r1978468 = exp(r1978467);
        double r1978469 = r1978466 / r1978468;
        double r1978470 = r1978466 * r1978468;
        double r1978471 = r1978469 + r1978470;
        double r1978472 = r1978465 * r1978471;
        return r1978472;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019170 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))