Average Error: 0.0 → 0.0
Time: 4.4s
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 r49487 = 0.5;
        double r49488 = re;
        double r49489 = cos(r49488);
        double r49490 = r49487 * r49489;
        double r49491 = im;
        double r49492 = -r49491;
        double r49493 = exp(r49492);
        double r49494 = exp(r49491);
        double r49495 = r49493 + r49494;
        double r49496 = r49490 * r49495;
        return r49496;
}
↓
double f(double re, double im) {
        double r49497 = 0.5;
        double r49498 = re;
        double r49499 = cos(r49498);
        double r49500 = r49497 * r49499;
        double r49501 = im;
        double r49502 = -r49501;
        double r49503 = exp(r49502);
        double r49504 = exp(r49501);
        double r49505 = r49503 + r49504;
        double r49506 = r49500 * r49505;
        return r49506;
}

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 2020018 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))