Average Error: 0.0 → 0.0
Time: 18.7s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5}{e^{im}} \cdot \cos re + \left(0.5 \cdot e^{im}\right) \cdot \cos re\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5}{e^{im}} \cdot \cos re + \left(0.5 \cdot e^{im}\right) \cdot \cos re
double f(double re, double im) {
        double r1739158 = 0.5;
        double r1739159 = re;
        double r1739160 = cos(r1739159);
        double r1739161 = r1739158 * r1739160;
        double r1739162 = im;
        double r1739163 = -r1739162;
        double r1739164 = exp(r1739163);
        double r1739165 = exp(r1739162);
        double r1739166 = r1739164 + r1739165;
        double r1739167 = r1739161 * r1739166;
        return r1739167;
}
↓
double f(double re, double im) {
        double r1739168 = 0.5;
        double r1739169 = im;
        double r1739170 = exp(r1739169);
        double r1739171 = r1739168 / r1739170;
        double r1739172 = re;
        double r1739173 = cos(r1739172);
        double r1739174 = r1739171 * r1739173;
        double r1739175 = r1739168 * r1739170;
        double r1739176 = r1739175 * r1739173;
        double r1739177 = r1739174 + r1739176;
        return r1739177;
}

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. Simplified0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019141 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))