Average Error: 0.0 → 0.0
Time: 18.9s
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 r1865023 = 0.5;
        double r1865024 = re;
        double r1865025 = cos(r1865024);
        double r1865026 = r1865023 * r1865025;
        double r1865027 = im;
        double r1865028 = -r1865027;
        double r1865029 = exp(r1865028);
        double r1865030 = exp(r1865027);
        double r1865031 = r1865029 + r1865030;
        double r1865032 = r1865026 * r1865031;
        return r1865032;
}
↓
double f(double re, double im) {
        double r1865033 = im;
        double r1865034 = exp(r1865033);
        double r1865035 = -r1865033;
        double r1865036 = exp(r1865035);
        double r1865037 = r1865034 + r1865036;
        double r1865038 = 0.5;
        double r1865039 = re;
        double r1865040 = cos(r1865039);
        double r1865041 = r1865038 * r1865040;
        double r1865042 = r1865037 * r1865041;
        return r1865042;
}

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