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 r42063 = 0.5;
        double r42064 = re;
        double r42065 = cos(r42064);
        double r42066 = r42063 * r42065;
        double r42067 = im;
        double r42068 = -r42067;
        double r42069 = exp(r42068);
        double r42070 = exp(r42067);
        double r42071 = r42069 + r42070;
        double r42072 = r42066 * r42071;
        return r42072;
}
↓
double f(double re, double im) {
        double r42073 = 0.5;
        double r42074 = re;
        double r42075 = cos(r42074);
        double r42076 = r42073 * r42075;
        double r42077 = im;
        double r42078 = exp(r42077);
        double r42079 = r42076 / r42078;
        double r42080 = r42076 * r42078;
        double r42081 = r42079 + r42080;
        return r42081;
}

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 2020056 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))