Average Error: 0.0 → 0.0
Time: 12.4s
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 r3787590 = 0.5;
        double r3787591 = re;
        double r3787592 = cos(r3787591);
        double r3787593 = r3787590 * r3787592;
        double r3787594 = im;
        double r3787595 = -r3787594;
        double r3787596 = exp(r3787595);
        double r3787597 = exp(r3787594);
        double r3787598 = r3787596 + r3787597;
        double r3787599 = r3787593 * r3787598;
        return r3787599;
}
↓
double f(double re, double im) {
        double r3787600 = im;
        double r3787601 = exp(r3787600);
        double r3787602 = -r3787600;
        double r3787603 = exp(r3787602);
        double r3787604 = r3787601 + r3787603;
        double r3787605 = 0.5;
        double r3787606 = re;
        double r3787607 = cos(r3787606);
        double r3787608 = r3787605 * r3787607;
        double r3787609 = r3787604 * r3787608;
        return r3787609;
}

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 2019162 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))