Average Error: 0.0 → 0.0
Time: 14.6s
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 r27925 = 0.5;
        double r27926 = re;
        double r27927 = cos(r27926);
        double r27928 = r27925 * r27927;
        double r27929 = im;
        double r27930 = -r27929;
        double r27931 = exp(r27930);
        double r27932 = exp(r27929);
        double r27933 = r27931 + r27932;
        double r27934 = r27928 * r27933;
        return r27934;
}
↓
double f(double re, double im) {
        double r27935 = 0.5;
        double r27936 = re;
        double r27937 = cos(r27936);
        double r27938 = r27935 * r27937;
        double r27939 = im;
        double r27940 = -r27939;
        double r27941 = exp(r27940);
        double r27942 = exp(r27939);
        double r27943 = r27941 + r27942;
        double r27944 = r27938 * r27943;
        return r27944;
}

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 2019306 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))