Average Error: 0.0 → 0.0
Time: 3.7s
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 r50555 = 0.5;
        double r50556 = re;
        double r50557 = cos(r50556);
        double r50558 = r50555 * r50557;
        double r50559 = im;
        double r50560 = -r50559;
        double r50561 = exp(r50560);
        double r50562 = exp(r50559);
        double r50563 = r50561 + r50562;
        double r50564 = r50558 * r50563;
        return r50564;
}
↓
double f(double re, double im) {
        double r50565 = 0.5;
        double r50566 = re;
        double r50567 = cos(r50566);
        double r50568 = r50565 * r50567;
        double r50569 = im;
        double r50570 = -r50569;
        double r50571 = exp(r50570);
        double r50572 = exp(r50569);
        double r50573 = r50571 + r50572;
        double r50574 = r50568 * r50573;
        return r50574;
}

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 2019351 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))