Average Error: 0.0 → 0.0
Time: 4.9s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \cos re}{e^{im}} + \left(\left(0.5 \cdot \cos re\right) \cdot \sqrt{e^{im}}\right) \cdot \sqrt{e^{im}}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5 \cdot \cos re}{e^{im}} + \left(\left(0.5 \cdot \cos re\right) \cdot \sqrt{e^{im}}\right) \cdot \sqrt{e^{im}}
double f(double re, double im) {
        double r52793 = 0.5;
        double r52794 = re;
        double r52795 = cos(r52794);
        double r52796 = r52793 * r52795;
        double r52797 = im;
        double r52798 = -r52797;
        double r52799 = exp(r52798);
        double r52800 = exp(r52797);
        double r52801 = r52799 + r52800;
        double r52802 = r52796 * r52801;
        return r52802;
}
↓
double f(double re, double im) {
        double r52803 = 0.5;
        double r52804 = re;
        double r52805 = cos(r52804);
        double r52806 = r52803 * r52805;
        double r52807 = im;
        double r52808 = exp(r52807);
        double r52809 = r52806 / r52808;
        double r52810 = sqrt(r52808);
        double r52811 = r52806 * r52810;
        double r52812 = r52811 * r52810;
        double r52813 = r52809 + r52812;
        return r52813;
}

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. Using strategy rm

  6. Applied add-sqr-sqrt0.0

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

  7. Applied associate-*r*0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))