Average Error: 0.0 → 0.0
Time: 16.3s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)
double f(double re, double im) {
        double r2234395 = 0.5;
        double r2234396 = re;
        double r2234397 = cos(r2234396);
        double r2234398 = r2234395 * r2234397;
        double r2234399 = im;
        double r2234400 = -r2234399;
        double r2234401 = exp(r2234400);
        double r2234402 = exp(r2234399);
        double r2234403 = r2234401 + r2234402;
        double r2234404 = r2234398 * r2234403;
        return r2234404;
}
↓
double f(double re, double im) {
        double r2234405 = im;
        double r2234406 = exp(r2234405);
        double r2234407 = -r2234405;
        double r2234408 = exp(r2234407);
        double r2234409 = r2234406 + r2234408;
        double r2234410 = 0.5;
        double r2234411 = re;
        double r2234412 = cos(r2234411);
        double r2234413 = r2234410 * r2234412;
        double r2234414 = r2234409 * r2234413;
        return r2234414;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))