Average Error: 0.0 → 0.0
Time: 25.1s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(\cos re \cdot 0.5\right) \cdot e^{im} + \frac{0.5}{e^{im}} \cdot \cos re\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(\cos re \cdot 0.5\right) \cdot e^{im} + \frac{0.5}{e^{im}} \cdot \cos re
double f(double re, double im) {
        double r3644805 = 0.5;
        double r3644806 = re;
        double r3644807 = cos(r3644806);
        double r3644808 = r3644805 * r3644807;
        double r3644809 = im;
        double r3644810 = -r3644809;
        double r3644811 = exp(r3644810);
        double r3644812 = exp(r3644809);
        double r3644813 = r3644811 + r3644812;
        double r3644814 = r3644808 * r3644813;
        return r3644814;
}
↓
double f(double re, double im) {
        double r3644815 = re;
        double r3644816 = cos(r3644815);
        double r3644817 = 0.5;
        double r3644818 = r3644816 * r3644817;
        double r3644819 = im;
        double r3644820 = exp(r3644819);
        double r3644821 = r3644818 * r3644820;
        double r3644822 = r3644817 / r3644820;
        double r3644823 = r3644822 * r3644816;
        double r3644824 = r3644821 + r3644823;
        return r3644824;
}

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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019125 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))