Average Error: 0.0 → 0.0
Time: 3.9s
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 r32123 = 0.5;
        double r32124 = re;
        double r32125 = cos(r32124);
        double r32126 = r32123 * r32125;
        double r32127 = im;
        double r32128 = -r32127;
        double r32129 = exp(r32128);
        double r32130 = exp(r32127);
        double r32131 = r32129 + r32130;
        double r32132 = r32126 * r32131;
        return r32132;
}
↓
double f(double re, double im) {
        double r32133 = 0.5;
        double r32134 = re;
        double r32135 = cos(r32134);
        double r32136 = r32133 * r32135;
        double r32137 = im;
        double r32138 = exp(r32137);
        double r32139 = r32136 / r32138;
        double r32140 = r32136 * r32138;
        double r32141 = r32139 + r32140;
        return r32141;
}

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 2020039 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))