Average Error: 0.0 → 0.0
Time: 7.8s
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 r59115 = 0.5;
        double r59116 = re;
        double r59117 = cos(r59116);
        double r59118 = r59115 * r59117;
        double r59119 = im;
        double r59120 = -r59119;
        double r59121 = exp(r59120);
        double r59122 = exp(r59119);
        double r59123 = r59121 + r59122;
        double r59124 = r59118 * r59123;
        return r59124;
}
↓
double f(double re, double im) {
        double r59125 = 0.5;
        double r59126 = re;
        double r59127 = cos(r59126);
        double r59128 = r59125 * r59127;
        double r59129 = im;
        double r59130 = -r59129;
        double r59131 = exp(r59130);
        double r59132 = exp(r59129);
        double r59133 = r59131 + r59132;
        double r59134 = r59128 * r59133;
        return r59134;
}

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 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))