Average Error: 0.0 → 0.0
Time: 5.0s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r41503 = 0.5;
        double r41504 = re;
        double r41505 = cos(r41504);
        double r41506 = r41503 * r41505;
        double r41507 = im;
        double r41508 = -r41507;
        double r41509 = exp(r41508);
        double r41510 = exp(r41507);
        double r41511 = r41509 + r41510;
        double r41512 = r41506 * r41511;
        return r41512;
}
↓
double f(double re, double im) {
        double r41513 = 0.5;
        double r41514 = re;
        double r41515 = cos(r41514);
        double r41516 = r41513 * r41515;
        double r41517 = im;
        double r41518 = -r41517;
        double r41519 = exp(r41518);
        double r41520 = exp(r41517);
        double r41521 = r41519 + r41520;
        double r41522 = r41516 * r41521;
        return r41522;
}

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

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

Reproduce

herbie shell --seed 2019354 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))