Average Error: 0.0 → 0.0
Time: 7.7s
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 r55118 = 0.5;
        double r55119 = re;
        double r55120 = cos(r55119);
        double r55121 = r55118 * r55120;
        double r55122 = im;
        double r55123 = -r55122;
        double r55124 = exp(r55123);
        double r55125 = exp(r55122);
        double r55126 = r55124 + r55125;
        double r55127 = r55121 * r55126;
        return r55127;
}
↓
double f(double re, double im) {
        double r55128 = 0.5;
        double r55129 = re;
        double r55130 = cos(r55129);
        double r55131 = r55128 * r55130;
        double r55132 = im;
        double r55133 = -r55132;
        double r55134 = exp(r55133);
        double r55135 = exp(r55132);
        double r55136 = r55134 + r55135;
        double r55137 = r55131 * r55136;
        return r55137;
}

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 2020043 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))