Average Error: 0.0 → 0.0
Time: 7.8s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)
double f(double re, double im) {
        double r58600 = 0.5;
        double r58601 = re;
        double r58602 = cos(r58601);
        double r58603 = r58600 * r58602;
        double r58604 = im;
        double r58605 = -r58604;
        double r58606 = exp(r58605);
        double r58607 = exp(r58604);
        double r58608 = r58606 + r58607;
        double r58609 = r58603 * r58608;
        return r58609;
}
↓
double f(double re, double im) {
        double r58610 = re;
        double r58611 = cos(r58610);
        double r58612 = im;
        double r58613 = exp(r58612);
        double r58614 = 0.5;
        double r58615 = r58613 * r58614;
        double r58616 = r58614 / r58613;
        double r58617 = r58615 + r58616;
        double r58618 = r58611 * r58617;
        return r58618;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019308 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))