Average Error: 0.0 → 0.0
Time: 15.8s
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 r35126 = 0.5;
        double r35127 = re;
        double r35128 = cos(r35127);
        double r35129 = r35126 * r35128;
        double r35130 = im;
        double r35131 = -r35130;
        double r35132 = exp(r35131);
        double r35133 = exp(r35130);
        double r35134 = r35132 + r35133;
        double r35135 = r35129 * r35134;
        return r35135;
}
↓
double f(double re, double im) {
        double r35136 = 0.5;
        double r35137 = re;
        double r35138 = cos(r35137);
        double r35139 = r35136 * r35138;
        double r35140 = im;
        double r35141 = exp(r35140);
        double r35142 = r35139 / r35141;
        double r35143 = r35139 * r35141;
        double r35144 = r35142 + r35143;
        return r35144;
}

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 2019303 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))