Average Error: 0.0 → 0.0
Time: 4.0s
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 r51181 = 0.5;
        double r51182 = re;
        double r51183 = cos(r51182);
        double r51184 = r51181 * r51183;
        double r51185 = im;
        double r51186 = -r51185;
        double r51187 = exp(r51186);
        double r51188 = exp(r51185);
        double r51189 = r51187 + r51188;
        double r51190 = r51184 * r51189;
        return r51190;
}
↓
double f(double re, double im) {
        double r51191 = 0.5;
        double r51192 = re;
        double r51193 = cos(r51192);
        double r51194 = r51191 * r51193;
        double r51195 = im;
        double r51196 = -r51195;
        double r51197 = exp(r51196);
        double r51198 = exp(r51195);
        double r51199 = r51197 + r51198;
        double r51200 = r51194 * r51199;
        return r51200;
}

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))))