Average Error: 0.0 → 0.0
Time: 13.8s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[e^{im} \cdot \left(0.5 \cdot \cos re\right) + \frac{\cos re}{e^{im}} \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
e^{im} \cdot \left(0.5 \cdot \cos re\right) + \frac{\cos re}{e^{im}} \cdot 0.5
double f(double re, double im) {
        double r31711 = 0.5;
        double r31712 = re;
        double r31713 = cos(r31712);
        double r31714 = r31711 * r31713;
        double r31715 = im;
        double r31716 = -r31715;
        double r31717 = exp(r31716);
        double r31718 = exp(r31715);
        double r31719 = r31717 + r31718;
        double r31720 = r31714 * r31719;
        return r31720;
}
↓
double f(double re, double im) {
        double r31721 = im;
        double r31722 = exp(r31721);
        double r31723 = 0.5;
        double r31724 = re;
        double r31725 = cos(r31724);
        double r31726 = r31723 * r31725;
        double r31727 = r31722 * r31726;
        double r31728 = r31725 / r31722;
        double r31729 = r31728 * r31723;
        double r31730 = r31727 + r31729;
        return r31730;
}

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

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))