Average Error: 0.0 → 0.0
Time: 22.2s
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 r1511320 = 0.5;
        double r1511321 = re;
        double r1511322 = cos(r1511321);
        double r1511323 = r1511320 * r1511322;
        double r1511324 = im;
        double r1511325 = -r1511324;
        double r1511326 = exp(r1511325);
        double r1511327 = exp(r1511324);
        double r1511328 = r1511326 + r1511327;
        double r1511329 = r1511323 * r1511328;
        return r1511329;
}
↓
double f(double re, double im) {
        double r1511330 = re;
        double r1511331 = cos(r1511330);
        double r1511332 = 0.5;
        double r1511333 = im;
        double r1511334 = exp(r1511333);
        double r1511335 = r1511332 / r1511334;
        double r1511336 = r1511332 * r1511334;
        double r1511337 = r1511335 + r1511336;
        double r1511338 = r1511331 * r1511337;
        return r1511338;
}

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 2019119 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))