Average Error: 0.0 → 0.0
Time: 19.4s
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 r31389 = 0.5;
        double r31390 = re;
        double r31391 = cos(r31390);
        double r31392 = r31389 * r31391;
        double r31393 = im;
        double r31394 = -r31393;
        double r31395 = exp(r31394);
        double r31396 = exp(r31393);
        double r31397 = r31395 + r31396;
        double r31398 = r31392 * r31397;
        return r31398;
}
↓
double f(double re, double im) {
        double r31399 = 0.5;
        double r31400 = re;
        double r31401 = cos(r31400);
        double r31402 = r31399 * r31401;
        double r31403 = im;
        double r31404 = -r31403;
        double r31405 = exp(r31404);
        double r31406 = exp(r31403);
        double r31407 = r31405 + r31406;
        double r31408 = r31402 * r31407;
        return r31408;
}

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 2019325 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))