Average Error: 0.0 → 0.0
Time: 14.7s
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 r26360 = 0.5;
        double r26361 = re;
        double r26362 = cos(r26361);
        double r26363 = r26360 * r26362;
        double r26364 = im;
        double r26365 = -r26364;
        double r26366 = exp(r26365);
        double r26367 = exp(r26364);
        double r26368 = r26366 + r26367;
        double r26369 = r26363 * r26368;
        return r26369;
}
↓
double f(double re, double im) {
        double r26370 = 0.5;
        double r26371 = re;
        double r26372 = cos(r26371);
        double r26373 = r26370 * r26372;
        double r26374 = im;
        double r26375 = -r26374;
        double r26376 = exp(r26375);
        double r26377 = exp(r26374);
        double r26378 = r26376 + r26377;
        double r26379 = r26373 * r26378;
        return r26379;
}

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 2019212 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))