Average Error: 0.0 → 0.0
Time: 5.5s
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 r57743 = 0.5;
        double r57744 = re;
        double r57745 = cos(r57744);
        double r57746 = r57743 * r57745;
        double r57747 = im;
        double r57748 = -r57747;
        double r57749 = exp(r57748);
        double r57750 = exp(r57747);
        double r57751 = r57749 + r57750;
        double r57752 = r57746 * r57751;
        return r57752;
}
↓
double f(double re, double im) {
        double r57753 = 0.5;
        double r57754 = re;
        double r57755 = cos(r57754);
        double r57756 = r57753 * r57755;
        double r57757 = im;
        double r57758 = -r57757;
        double r57759 = exp(r57758);
        double r57760 = exp(r57757);
        double r57761 = r57759 + r57760;
        double r57762 = r57756 * r57761;
        return r57762;
}

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 2020089 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))