Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r33758 = 0.5;
        double r33759 = re;
        double r33760 = cos(r33759);
        double r33761 = r33758 * r33760;
        double r33762 = im;
        double r33763 = -r33762;
        double r33764 = exp(r33763);
        double r33765 = exp(r33762);
        double r33766 = r33764 + r33765;
        double r33767 = r33761 * r33766;
        return r33767;
}
↓
double f(double re, double im) {
        double r33768 = 0.5;
        double r33769 = re;
        double r33770 = cos(r33769);
        double r33771 = r33768 * r33770;
        double r33772 = im;
        double r33773 = -r33772;
        double r33774 = exp(r33773);
        double r33775 = exp(r33772);
        double r33776 = r33774 + r33775;
        double r33777 = r33771 * r33776;
        return r33777;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))