Average Error: 0.0 → 0.0
Time: 11.4s
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 r1669591 = 0.5;
        double r1669592 = re;
        double r1669593 = cos(r1669592);
        double r1669594 = r1669591 * r1669593;
        double r1669595 = im;
        double r1669596 = -r1669595;
        double r1669597 = exp(r1669596);
        double r1669598 = exp(r1669595);
        double r1669599 = r1669597 + r1669598;
        double r1669600 = r1669594 * r1669599;
        return r1669600;
}
↓
double f(double re, double im) {
        double r1669601 = im;
        double r1669602 = exp(r1669601);
        double r1669603 = -r1669601;
        double r1669604 = exp(r1669603);
        double r1669605 = r1669602 + r1669604;
        double r1669606 = 0.5;
        double r1669607 = re;
        double r1669608 = cos(r1669607);
        double r1669609 = r1669606 * r1669608;
        double r1669610 = r1669605 * r1669609;
        return r1669610;
}

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 2019121 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))