Average Error: 0.0 → 0.0
Time: 3.7s
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 r51210 = 0.5;
        double r51211 = re;
        double r51212 = cos(r51211);
        double r51213 = r51210 * r51212;
        double r51214 = im;
        double r51215 = -r51214;
        double r51216 = exp(r51215);
        double r51217 = exp(r51214);
        double r51218 = r51216 + r51217;
        double r51219 = r51213 * r51218;
        return r51219;
}
↓
double f(double re, double im) {
        double r51220 = 0.5;
        double r51221 = re;
        double r51222 = cos(r51221);
        double r51223 = r51220 * r51222;
        double r51224 = im;
        double r51225 = -r51224;
        double r51226 = exp(r51225);
        double r51227 = exp(r51224);
        double r51228 = r51226 + r51227;
        double r51229 = r51223 * r51228;
        return r51229;
}

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 2020001 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))