Average Error: 0.0 → 0.0
Time: 7.2s
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 r52941 = 0.5;
        double r52942 = re;
        double r52943 = cos(r52942);
        double r52944 = r52941 * r52943;
        double r52945 = im;
        double r52946 = -r52945;
        double r52947 = exp(r52946);
        double r52948 = exp(r52945);
        double r52949 = r52947 + r52948;
        double r52950 = r52944 * r52949;
        return r52950;
}
↓
double f(double re, double im) {
        double r52951 = 0.5;
        double r52952 = re;
        double r52953 = cos(r52952);
        double r52954 = r52951 * r52953;
        double r52955 = im;
        double r52956 = -r52955;
        double r52957 = exp(r52956);
        double r52958 = exp(r52955);
        double r52959 = r52957 + r52958;
        double r52960 = r52954 * r52959;
        return r52960;
}

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 2020043 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))