Average Error: 0.0 → 0.0
Time: 4.3s
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 r54393 = 0.5;
        double r54394 = re;
        double r54395 = cos(r54394);
        double r54396 = r54393 * r54395;
        double r54397 = im;
        double r54398 = -r54397;
        double r54399 = exp(r54398);
        double r54400 = exp(r54397);
        double r54401 = r54399 + r54400;
        double r54402 = r54396 * r54401;
        return r54402;
}
↓
double f(double re, double im) {
        double r54403 = 0.5;
        double r54404 = re;
        double r54405 = cos(r54404);
        double r54406 = r54403 * r54405;
        double r54407 = im;
        double r54408 = -r54407;
        double r54409 = exp(r54408);
        double r54410 = exp(r54407);
        double r54411 = r54409 + r54410;
        double r54412 = r54406 * r54411;
        return r54412;
}

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 2020065 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))