Average Error: 0.0 → 0.0
Time: 9.8s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right)
double f(double re, double im) {
        double r737476 = 0.5;
        double r737477 = re;
        double r737478 = cos(r737477);
        double r737479 = r737476 * r737478;
        double r737480 = im;
        double r737481 = -r737480;
        double r737482 = exp(r737481);
        double r737483 = exp(r737480);
        double r737484 = r737482 + r737483;
        double r737485 = r737479 * r737484;
        return r737485;
}
↓
double f(double re, double im) {
        double r737486 = re;
        double r737487 = cos(r737486);
        double r737488 = 0.5;
        double r737489 = im;
        double r737490 = exp(r737489);
        double r737491 = r737488 / r737490;
        double r737492 = r737490 * r737488;
        double r737493 = r737491 + r737492;
        double r737494 = r737487 * r737493;
        return r737494;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\cos re \cdot \left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right)}\]

  3. Final simplification0.0

    \[\leadsto \cos re \cdot \left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right)\]

Reproduce

herbie shell --seed 2019152 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))