Average Error: 0.0 → 0.0
Time: 3.9s
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 r32033 = 0.5;
        double r32034 = re;
        double r32035 = cos(r32034);
        double r32036 = r32033 * r32035;
        double r32037 = im;
        double r32038 = -r32037;
        double r32039 = exp(r32038);
        double r32040 = exp(r32037);
        double r32041 = r32039 + r32040;
        double r32042 = r32036 * r32041;
        return r32042;
}
↓
double f(double re, double im) {
        double r32043 = 0.5;
        double r32044 = re;
        double r32045 = cos(r32044);
        double r32046 = r32043 * r32045;
        double r32047 = im;
        double r32048 = -r32047;
        double r32049 = exp(r32048);
        double r32050 = exp(r32047);
        double r32051 = r32049 + r32050;
        double r32052 = r32046 * r32051;
        return r32052;
}

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 2019353 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))