Average Error: 0.0 → 0.0
Time: 13.1s
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 r45123 = 0.5;
        double r45124 = re;
        double r45125 = cos(r45124);
        double r45126 = r45123 * r45125;
        double r45127 = im;
        double r45128 = -r45127;
        double r45129 = exp(r45128);
        double r45130 = exp(r45127);
        double r45131 = r45129 + r45130;
        double r45132 = r45126 * r45131;
        return r45132;
}
↓
double f(double re, double im) {
        double r45133 = 0.5;
        double r45134 = re;
        double r45135 = cos(r45134);
        double r45136 = r45133 * r45135;
        double r45137 = im;
        double r45138 = -r45137;
        double r45139 = exp(r45138);
        double r45140 = exp(r45137);
        double r45141 = r45139 + r45140;
        double r45142 = r45136 * r45141;
        return r45142;
}

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 2019298 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))