Average Error: 0.0 → 0.0
Time: 14.8s
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 r2911308 = 0.5;
        double r2911309 = re;
        double r2911310 = cos(r2911309);
        double r2911311 = r2911308 * r2911310;
        double r2911312 = im;
        double r2911313 = -r2911312;
        double r2911314 = exp(r2911313);
        double r2911315 = exp(r2911312);
        double r2911316 = r2911314 + r2911315;
        double r2911317 = r2911311 * r2911316;
        return r2911317;
}
↓
double f(double re, double im) {
        double r2911318 = 0.5;
        double r2911319 = im;
        double r2911320 = exp(r2911319);
        double r2911321 = r2911318 / r2911320;
        double r2911322 = re;
        double r2911323 = cos(r2911322);
        double r2911324 = r2911321 * r2911323;
        double r2911325 = r2911318 * r2911320;
        double r2911326 = r2911325 * r2911323;
        double r2911327 = r2911324 + r2911326;
        return r2911327;
}

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 2019172 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))