Average Error: 0.0 → 0.0
Time: 22.8s
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 r3020646 = 0.5;
        double r3020647 = re;
        double r3020648 = cos(r3020647);
        double r3020649 = r3020646 * r3020648;
        double r3020650 = im;
        double r3020651 = -r3020650;
        double r3020652 = exp(r3020651);
        double r3020653 = exp(r3020650);
        double r3020654 = r3020652 + r3020653;
        double r3020655 = r3020649 * r3020654;
        return r3020655;
}
↓
double f(double re, double im) {
        double r3020656 = re;
        double r3020657 = cos(r3020656);
        double r3020658 = 0.5;
        double r3020659 = im;
        double r3020660 = exp(r3020659);
        double r3020661 = r3020658 / r3020660;
        double r3020662 = r3020658 * r3020660;
        double r3020663 = r3020661 + r3020662;
        double r3020664 = r3020657 * r3020663;
        return r3020664;
}

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 2019164 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))