Average Error: 0.0 → 0.0
Time: 19.0s
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 r45638 = 0.5;
        double r45639 = re;
        double r45640 = cos(r45639);
        double r45641 = r45638 * r45640;
        double r45642 = im;
        double r45643 = -r45642;
        double r45644 = exp(r45643);
        double r45645 = exp(r45642);
        double r45646 = r45644 + r45645;
        double r45647 = r45641 * r45646;
        return r45647;
}
↓
double f(double re, double im) {
        double r45648 = 0.5;
        double r45649 = re;
        double r45650 = cos(r45649);
        double r45651 = r45648 * r45650;
        double r45652 = im;
        double r45653 = -r45652;
        double r45654 = exp(r45653);
        double r45655 = exp(r45652);
        double r45656 = r45654 + r45655;
        double r45657 = r45651 * r45656;
        return r45657;
}

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 2019323 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))