Average Error: 0.0 → 0.0
Time: 10.5s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)
double f(double re, double im) {
        double r29044 = 0.5;
        double r29045 = re;
        double r29046 = cos(r29045);
        double r29047 = r29044 * r29046;
        double r29048 = im;
        double r29049 = -r29048;
        double r29050 = exp(r29049);
        double r29051 = exp(r29048);
        double r29052 = r29050 + r29051;
        double r29053 = r29047 * r29052;
        return r29053;
}
↓
double f(double re, double im) {
        double r29054 = re;
        double r29055 = cos(r29054);
        double r29056 = im;
        double r29057 = exp(r29056);
        double r29058 = 0.5;
        double r29059 = r29057 * r29058;
        double r29060 = r29058 / r29057;
        double r29061 = r29059 + r29060;
        double r29062 = r29055 * r29061;
        return r29062;
}

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

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

Reproduce

herbie shell --seed 2019297 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))