Average Error: 0.0 → 0.0
Time: 2.8s
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 r46935 = 0.5;
        double r46936 = re;
        double r46937 = cos(r46936);
        double r46938 = r46935 * r46937;
        double r46939 = im;
        double r46940 = -r46939;
        double r46941 = exp(r46940);
        double r46942 = exp(r46939);
        double r46943 = r46941 + r46942;
        double r46944 = r46938 * r46943;
        return r46944;
}
↓
double f(double re, double im) {
        double r46945 = 0.5;
        double r46946 = re;
        double r46947 = cos(r46946);
        double r46948 = r46945 * r46947;
        double r46949 = im;
        double r46950 = -r46949;
        double r46951 = exp(r46950);
        double r46952 = exp(r46949);
        double r46953 = r46951 + r46952;
        double r46954 = r46948 * r46953;
        return r46954;
}

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 2020021 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))