Average Error: 0.0 → 0.0
Time: 5.4s
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 r264 = 0.5;
        double r265 = re;
        double r266 = cos(r265);
        double r267 = r264 * r266;
        double r268 = im;
        double r269 = -r268;
        double r270 = exp(r269);
        double r271 = exp(r268);
        double r272 = r270 + r271;
        double r273 = r267 * r272;
        return r273;
}
↓
double f(double re, double im) {
        double r274 = 0.5;
        double r275 = re;
        double r276 = cos(r275);
        double r277 = r274 * r276;
        double r278 = im;
        double r279 = exp(r278);
        double r280 = r277 / r279;
        double r281 = r277 * r279;
        double r282 = r280 + r281;
        return r282;
}

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 2020025 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))