Average Error: 0.0 → 0.0
Time: 15.3s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)
double f(double re, double im) {
        double r1807775 = 0.5;
        double r1807776 = re;
        double r1807777 = cos(r1807776);
        double r1807778 = r1807775 * r1807777;
        double r1807779 = im;
        double r1807780 = -r1807779;
        double r1807781 = exp(r1807780);
        double r1807782 = exp(r1807779);
        double r1807783 = r1807781 + r1807782;
        double r1807784 = r1807778 * r1807783;
        return r1807784;
}
↓
double f(double re, double im) {
        double r1807785 = re;
        double r1807786 = cos(r1807785);
        double r1807787 = 0.5;
        double r1807788 = im;
        double r1807789 = exp(r1807788);
        double r1807790 = r1807787 / r1807789;
        double r1807791 = r1807787 * r1807789;
        double r1807792 = r1807790 + r1807791;
        double r1807793 = r1807786 * r1807792;
        return r1807793;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))