Average Error: 0.0 → 0.0
Time: 4.4s
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 r32814 = 0.5;
        double r32815 = re;
        double r32816 = cos(r32815);
        double r32817 = r32814 * r32816;
        double r32818 = im;
        double r32819 = -r32818;
        double r32820 = exp(r32819);
        double r32821 = exp(r32818);
        double r32822 = r32820 + r32821;
        double r32823 = r32817 * r32822;
        return r32823;
}
↓
double f(double re, double im) {
        double r32824 = 0.5;
        double r32825 = re;
        double r32826 = cos(r32825);
        double r32827 = r32824 * r32826;
        double r32828 = im;
        double r32829 = exp(r32828);
        double r32830 = r32827 / r32829;
        double r32831 = r32827 * r32829;
        double r32832 = r32830 + r32831;
        return r32832;
}

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 2019352 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))