Average Error: 0.0 → 0.0
Time: 4.6s
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 r52162 = 0.5;
        double r52163 = re;
        double r52164 = cos(r52163);
        double r52165 = r52162 * r52164;
        double r52166 = im;
        double r52167 = -r52166;
        double r52168 = exp(r52167);
        double r52169 = exp(r52166);
        double r52170 = r52168 + r52169;
        double r52171 = r52165 * r52170;
        return r52171;
}
↓
double f(double re, double im) {
        double r52172 = 0.5;
        double r52173 = re;
        double r52174 = cos(r52173);
        double r52175 = r52172 * r52174;
        double r52176 = im;
        double r52177 = exp(r52176);
        double r52178 = r52175 / r52177;
        double r52179 = r52175 * r52177;
        double r52180 = r52178 + r52179;
        return r52180;
}

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 2020060 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))