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 r46485 = 0.5;
        double r46486 = re;
        double r46487 = cos(r46486);
        double r46488 = r46485 * r46487;
        double r46489 = im;
        double r46490 = -r46489;
        double r46491 = exp(r46490);
        double r46492 = exp(r46489);
        double r46493 = r46491 + r46492;
        double r46494 = r46488 * r46493;
        return r46494;
}
↓
double f(double re, double im) {
        double r46495 = 0.5;
        double r46496 = re;
        double r46497 = cos(r46496);
        double r46498 = r46495 * r46497;
        double r46499 = im;
        double r46500 = -r46499;
        double r46501 = exp(r46500);
        double r46502 = exp(r46499);
        double r46503 = r46501 + r46502;
        double r46504 = r46498 * r46503;
        return r46504;
}

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 2019351 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))