Average Error: 0.0 → 0.0
Time: 14.9s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(\cos re \cdot e^{im} + \frac{\cos re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(\cos re \cdot e^{im} + \frac{\cos re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r1086390 = 0.5;
        double r1086391 = re;
        double r1086392 = cos(r1086391);
        double r1086393 = r1086390 * r1086392;
        double r1086394 = im;
        double r1086395 = -r1086394;
        double r1086396 = exp(r1086395);
        double r1086397 = exp(r1086394);
        double r1086398 = r1086396 + r1086397;
        double r1086399 = r1086393 * r1086398;
        return r1086399;
}
↓
double f(double re, double im) {
        double r1086400 = re;
        double r1086401 = cos(r1086400);
        double r1086402 = im;
        double r1086403 = exp(r1086402);
        double r1086404 = r1086401 * r1086403;
        double r1086405 = r1086401 / r1086403;
        double r1086406 = r1086404 + r1086405;
        double r1086407 = 0.5;
        double r1086408 = r1086406 * r1086407;
        return r1086408;
}

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 associate-*l*0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019133 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))