Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}
double f(double re, double im) {
        double r36957 = 0.5;
        double r36958 = re;
        double r36959 = cos(r36958);
        double r36960 = r36957 * r36959;
        double r36961 = im;
        double r36962 = -r36961;
        double r36963 = exp(r36962);
        double r36964 = exp(r36961);
        double r36965 = r36963 + r36964;
        double r36966 = r36960 * r36965;
        return r36966;
}
↓
double f(double re, double im) {
        double r36967 = 0.5;
        double r36968 = re;
        double r36969 = cos(r36968);
        double r36970 = r36967 * r36969;
        double r36971 = im;
        double r36972 = exp(r36971);
        double r36973 = r36970 / r36972;
        double r36974 = r36970 * r36972;
        double r36975 = r36973 + r36974;
        return r36975;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \cos re\right) \cdot e^{-im} + \left(0.5 \cdot \cos re\right) \cdot e^{im}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\frac{0.5 \cdot \cos re}{e^{im}}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]

  5. Final simplification0.0

    \[\leadsto \frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]

Reproduce

herbie shell --seed 2019350 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))