Average Error: 0.0 → 0.0
Time: 5.6s
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 r51415 = 0.5;
        double r51416 = re;
        double r51417 = cos(r51416);
        double r51418 = r51415 * r51417;
        double r51419 = im;
        double r51420 = -r51419;
        double r51421 = exp(r51420);
        double r51422 = exp(r51419);
        double r51423 = r51421 + r51422;
        double r51424 = r51418 * r51423;
        return r51424;
}
↓
double f(double re, double im) {
        double r51425 = 0.5;
        double r51426 = re;
        double r51427 = cos(r51426);
        double r51428 = r51425 * r51427;
        double r51429 = im;
        double r51430 = exp(r51429);
        double r51431 = r51428 / r51430;
        double r51432 = r51428 * r51430;
        double r51433 = r51431 + r51432;
        return r51433;
}

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 2020083 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))