Average Error: 0.0 → 0.0
Time: 17.3s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} \cdot \cos re + \frac{\cos re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} \cdot \cos re + \frac{\cos re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r2280129 = 0.5;
        double r2280130 = re;
        double r2280131 = cos(r2280130);
        double r2280132 = r2280129 * r2280131;
        double r2280133 = im;
        double r2280134 = -r2280133;
        double r2280135 = exp(r2280134);
        double r2280136 = exp(r2280133);
        double r2280137 = r2280135 + r2280136;
        double r2280138 = r2280132 * r2280137;
        return r2280138;
}
↓
double f(double re, double im) {
        double r2280139 = im;
        double r2280140 = exp(r2280139);
        double r2280141 = re;
        double r2280142 = cos(r2280141);
        double r2280143 = r2280140 * r2280142;
        double r2280144 = r2280142 / r2280140;
        double r2280145 = r2280143 + r2280144;
        double r2280146 = 0.5;
        double r2280147 = r2280145 * r2280146;
        return r2280147;
}

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 associate-*l*0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))