Average Error: 0.0 → 0.0
Time: 38.0s
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 r37095 = 0.5;
        double r37096 = re;
        double r37097 = cos(r37096);
        double r37098 = r37095 * r37097;
        double r37099 = im;
        double r37100 = -r37099;
        double r37101 = exp(r37100);
        double r37102 = exp(r37099);
        double r37103 = r37101 + r37102;
        double r37104 = r37098 * r37103;
        return r37104;
}
↓
double f(double re, double im) {
        double r37105 = 0.5;
        double r37106 = re;
        double r37107 = cos(r37106);
        double r37108 = r37105 * r37107;
        double r37109 = im;
        double r37110 = -r37109;
        double r37111 = exp(r37110);
        double r37112 = exp(r37109);
        double r37113 = r37111 + r37112;
        double r37114 = r37108 * r37113;
        return r37114;
}

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 2019323 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))