Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r48290 = 0.5;
        double r48291 = re;
        double r48292 = cos(r48291);
        double r48293 = r48290 * r48292;
        double r48294 = im;
        double r48295 = -r48294;
        double r48296 = exp(r48295);
        double r48297 = exp(r48294);
        double r48298 = r48296 + r48297;
        double r48299 = r48293 * r48298;
        return r48299;
}
↓
double f(double re, double im) {
        double r48300 = 0.5;
        double r48301 = re;
        double r48302 = cos(r48301);
        double r48303 = r48300 * r48302;
        double r48304 = im;
        double r48305 = -r48304;
        double r48306 = exp(r48305);
        double r48307 = exp(r48304);
        double r48308 = r48306 + r48307;
        double r48309 = r48303 * r48308;
        return r48309;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))