Average Error: 0.0 → 0.0
Time: 13.1s
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 r65961 = 0.5;
        double r65962 = re;
        double r65963 = cos(r65962);
        double r65964 = r65961 * r65963;
        double r65965 = im;
        double r65966 = -r65965;
        double r65967 = exp(r65966);
        double r65968 = exp(r65965);
        double r65969 = r65967 + r65968;
        double r65970 = r65964 * r65969;
        return r65970;
}
↓
double f(double re, double im) {
        double r65971 = 0.5;
        double r65972 = re;
        double r65973 = cos(r65972);
        double r65974 = r65971 * r65973;
        double r65975 = im;
        double r65976 = -r65975;
        double r65977 = exp(r65976);
        double r65978 = exp(r65975);
        double r65979 = r65977 + r65978;
        double r65980 = r65974 * r65979;
        return r65980;
}

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 2020042 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))