Average Error: 0.0 → 0.0
Time: 3.7s
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 r92759 = 0.5;
        double r92760 = re;
        double r92761 = cos(r92760);
        double r92762 = r92759 * r92761;
        double r92763 = im;
        double r92764 = -r92763;
        double r92765 = exp(r92764);
        double r92766 = exp(r92763);
        double r92767 = r92765 + r92766;
        double r92768 = r92762 * r92767;
        return r92768;
}
↓
double f(double re, double im) {
        double r92769 = 0.5;
        double r92770 = re;
        double r92771 = cos(r92770);
        double r92772 = r92769 * r92771;
        double r92773 = im;
        double r92774 = exp(r92773);
        double r92775 = r92772 / r92774;
        double r92776 = r92772 * r92774;
        double r92777 = r92775 + r92776;
        return r92777;
}

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 2019344 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))