Average Error: 0.0 → 0.0
Time: 13.0s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)
double f(double re, double im) {
        double r3252546 = 0.5;
        double r3252547 = re;
        double r3252548 = cos(r3252547);
        double r3252549 = r3252546 * r3252548;
        double r3252550 = im;
        double r3252551 = -r3252550;
        double r3252552 = exp(r3252551);
        double r3252553 = exp(r3252550);
        double r3252554 = r3252552 + r3252553;
        double r3252555 = r3252549 * r3252554;
        return r3252555;
}
↓
double f(double re, double im) {
        double r3252556 = im;
        double r3252557 = exp(r3252556);
        double r3252558 = -r3252556;
        double r3252559 = exp(r3252558);
        double r3252560 = r3252557 + r3252559;
        double r3252561 = 0.5;
        double r3252562 = re;
        double r3252563 = cos(r3252562);
        double r3252564 = r3252561 * r3252563;
        double r3252565 = r3252560 * r3252564;
        return r3252565;
}

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

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))