Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r37543 = 0.5;
        double r37544 = re;
        double r37545 = cos(r37544);
        double r37546 = r37543 * r37545;
        double r37547 = im;
        double r37548 = -r37547;
        double r37549 = exp(r37548);
        double r37550 = exp(r37547);
        double r37551 = r37549 + r37550;
        double r37552 = r37546 * r37551;
        return r37552;
}
↓
double f(double re, double im) {
        double r37553 = 0.5;
        double r37554 = re;
        double r37555 = cos(r37554);
        double r37556 = r37553 * r37555;
        double r37557 = im;
        double r37558 = -r37557;
        double r37559 = exp(r37558);
        double r37560 = exp(r37557);
        double r37561 = r37559 + r37560;
        double r37562 = r37556 * r37561;
        return r37562;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020003 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))