Average Error: 0.0 → 0.0
Time: 3.3s
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 r45314 = 0.5;
        double r45315 = re;
        double r45316 = cos(r45315);
        double r45317 = r45314 * r45316;
        double r45318 = im;
        double r45319 = -r45318;
        double r45320 = exp(r45319);
        double r45321 = exp(r45318);
        double r45322 = r45320 + r45321;
        double r45323 = r45317 * r45322;
        return r45323;
}
↓
double f(double re, double im) {
        double r45324 = 0.5;
        double r45325 = re;
        double r45326 = cos(r45325);
        double r45327 = r45324 * r45326;
        double r45328 = im;
        double r45329 = exp(r45328);
        double r45330 = r45327 / r45329;
        double r45331 = r45327 * r45329;
        double r45332 = r45330 + r45331;
        return r45332;
}

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 2020064 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))