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 r30699 = 0.5;
        double r30700 = re;
        double r30701 = cos(r30700);
        double r30702 = r30699 * r30701;
        double r30703 = im;
        double r30704 = -r30703;
        double r30705 = exp(r30704);
        double r30706 = exp(r30703);
        double r30707 = r30705 + r30706;
        double r30708 = r30702 * r30707;
        return r30708;
}
↓
double f(double re, double im) {
        double r30709 = 0.5;
        double r30710 = re;
        double r30711 = cos(r30710);
        double r30712 = r30709 * r30711;
        double r30713 = im;
        double r30714 = exp(r30713);
        double r30715 = r30712 / r30714;
        double r30716 = r30712 * r30714;
        double r30717 = r30715 + r30716;
        return r30717;
}

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 2020036 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))