Average Error: 0.0 → 0.0
Time: 14.1s
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 r40138 = 0.5;
        double r40139 = re;
        double r40140 = cos(r40139);
        double r40141 = r40138 * r40140;
        double r40142 = im;
        double r40143 = -r40142;
        double r40144 = exp(r40143);
        double r40145 = exp(r40142);
        double r40146 = r40144 + r40145;
        double r40147 = r40141 * r40146;
        return r40147;
}
↓
double f(double re, double im) {
        double r40148 = 0.5;
        double r40149 = re;
        double r40150 = cos(r40149);
        double r40151 = r40148 * r40150;
        double r40152 = im;
        double r40153 = -r40152;
        double r40154 = exp(r40153);
        double r40155 = exp(r40152);
        double r40156 = r40154 + r40155;
        double r40157 = r40151 * r40156;
        return r40157;
}

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 2019212 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))