Average Error: 0.0 → 0.0
Time: 3.4s
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 r34757 = 0.5;
        double r34758 = re;
        double r34759 = cos(r34758);
        double r34760 = r34757 * r34759;
        double r34761 = im;
        double r34762 = -r34761;
        double r34763 = exp(r34762);
        double r34764 = exp(r34761);
        double r34765 = r34763 + r34764;
        double r34766 = r34760 * r34765;
        return r34766;
}
↓
double f(double re, double im) {
        double r34767 = 0.5;
        double r34768 = re;
        double r34769 = cos(r34768);
        double r34770 = r34767 * r34769;
        double r34771 = im;
        double r34772 = exp(r34771);
        double r34773 = r34770 / r34772;
        double r34774 = r34770 * r34772;
        double r34775 = r34773 + r34774;
        return r34775;
}

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 2020057 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))