Average Error: 0.0 → 0.0
Time: 3.0s
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 r36449 = 0.5;
        double r36450 = re;
        double r36451 = cos(r36450);
        double r36452 = r36449 * r36451;
        double r36453 = im;
        double r36454 = -r36453;
        double r36455 = exp(r36454);
        double r36456 = exp(r36453);
        double r36457 = r36455 + r36456;
        double r36458 = r36452 * r36457;
        return r36458;
}
↓
double f(double re, double im) {
        double r36459 = 0.5;
        double r36460 = re;
        double r36461 = cos(r36460);
        double r36462 = r36459 * r36461;
        double r36463 = im;
        double r36464 = -r36463;
        double r36465 = exp(r36464);
        double r36466 = exp(r36463);
        double r36467 = r36465 + r36466;
        double r36468 = r36462 * r36467;
        return r36468;
}

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 2020002 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))