Average Error: 0.0 → 0.0
Time: 3.6s
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 r32405 = 0.5;
        double r32406 = re;
        double r32407 = cos(r32406);
        double r32408 = r32405 * r32407;
        double r32409 = im;
        double r32410 = -r32409;
        double r32411 = exp(r32410);
        double r32412 = exp(r32409);
        double r32413 = r32411 + r32412;
        double r32414 = r32408 * r32413;
        return r32414;
}
↓
double f(double re, double im) {
        double r32415 = 0.5;
        double r32416 = re;
        double r32417 = cos(r32416);
        double r32418 = r32415 * r32417;
        double r32419 = im;
        double r32420 = -r32419;
        double r32421 = exp(r32420);
        double r32422 = exp(r32419);
        double r32423 = r32421 + r32422;
        double r32424 = r32418 * r32423;
        return r32424;
}

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