Average Error: 0.0 → 0.0
Time: 18.9s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\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 r52853 = 0.5;
        double r52854 = re;
        double r52855 = cos(r52854);
        double r52856 = r52853 * r52855;
        double r52857 = im;
        double r52858 = -r52857;
        double r52859 = exp(r52858);
        double r52860 = exp(r52857);
        double r52861 = r52859 + r52860;
        double r52862 = r52856 * r52861;
        return r52862;
}
↓
double f(double re, double im) {
        double r52863 = 0.5;
        double r52864 = re;
        double r52865 = cos(r52864);
        double r52866 = r52863 * r52865;
        double r52867 = im;
        double r52868 = -r52867;
        double r52869 = exp(r52868);
        double r52870 = exp(r52867);
        double r52871 = r52869 + r52870;
        double r52872 = r52866 * r52871;
        return r52872;
}

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 2019325 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))