Average Error: 0.0 → 0.0
Time: 3.8s
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 r40494 = 0.5;
        double r40495 = re;
        double r40496 = cos(r40495);
        double r40497 = r40494 * r40496;
        double r40498 = im;
        double r40499 = -r40498;
        double r40500 = exp(r40499);
        double r40501 = exp(r40498);
        double r40502 = r40500 + r40501;
        double r40503 = r40497 * r40502;
        return r40503;
}
↓
double f(double re, double im) {
        double r40504 = 0.5;
        double r40505 = re;
        double r40506 = cos(r40505);
        double r40507 = r40504 * r40506;
        double r40508 = im;
        double r40509 = -r40508;
        double r40510 = exp(r40509);
        double r40511 = exp(r40508);
        double r40512 = r40510 + r40511;
        double r40513 = r40507 * r40512;
        return r40513;
}

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 2019356 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))