Average Error: 0.0 → 0.0
Time: 5.4s
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 r98024 = 0.5;
        double r98025 = re;
        double r98026 = cos(r98025);
        double r98027 = r98024 * r98026;
        double r98028 = im;
        double r98029 = -r98028;
        double r98030 = exp(r98029);
        double r98031 = exp(r98028);
        double r98032 = r98030 + r98031;
        double r98033 = r98027 * r98032;
        return r98033;
}
↓
double f(double re, double im) {
        double r98034 = 0.5;
        double r98035 = re;
        double r98036 = cos(r98035);
        double r98037 = r98034 * r98036;
        double r98038 = im;
        double r98039 = exp(r98038);
        double r98040 = r98037 / r98039;
        double r98041 = r98037 * r98039;
        double r98042 = r98040 + r98041;
        return r98042;
}

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 2020083 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))