Average Error: 0.0 → 0.0
Time: 13.4s
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 r28239 = 0.5;
        double r28240 = re;
        double r28241 = cos(r28240);
        double r28242 = r28239 * r28241;
        double r28243 = im;
        double r28244 = -r28243;
        double r28245 = exp(r28244);
        double r28246 = exp(r28243);
        double r28247 = r28245 + r28246;
        double r28248 = r28242 * r28247;
        return r28248;
}
↓
double f(double re, double im) {
        double r28249 = 0.5;
        double r28250 = re;
        double r28251 = cos(r28250);
        double r28252 = r28249 * r28251;
        double r28253 = im;
        double r28254 = -r28253;
        double r28255 = exp(r28254);
        double r28256 = exp(r28253);
        double r28257 = r28255 + r28256;
        double r28258 = r28252 * r28257;
        return r28258;
}

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 2019326 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))