Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}
double f(double re, double im) {
        double r44601 = 0.5;
        double r44602 = re;
        double r44603 = cos(r44602);
        double r44604 = r44601 * r44603;
        double r44605 = im;
        double r44606 = -r44605;
        double r44607 = exp(r44606);
        double r44608 = exp(r44605);
        double r44609 = r44607 + r44608;
        double r44610 = r44604 * r44609;
        return r44610;
}
↓
double f(double re, double im) {
        double r44611 = 0.5;
        double r44612 = re;
        double r44613 = cos(r44612);
        double r44614 = r44611 * r44613;
        double r44615 = im;
        double r44616 = exp(r44615);
        double r44617 = r44614 / r44616;
        double r44618 = r44614 * r44616;
        double r44619 = r44617 + r44618;
        return r44619;
}

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

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

Reproduce

herbie shell --seed 2020064 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))