Average Error: 0.0 → 0.0
Time: 18.8s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[0.5 \cdot \frac{\cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
0.5 \cdot \frac{\cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}
double f(double re, double im) {
        double r41174 = 0.5;
        double r41175 = re;
        double r41176 = cos(r41175);
        double r41177 = r41174 * r41176;
        double r41178 = im;
        double r41179 = -r41178;
        double r41180 = exp(r41179);
        double r41181 = exp(r41178);
        double r41182 = r41180 + r41181;
        double r41183 = r41177 * r41182;
        return r41183;
}
↓
double f(double re, double im) {
        double r41184 = 0.5;
        double r41185 = re;
        double r41186 = cos(r41185);
        double r41187 = im;
        double r41188 = exp(r41187);
        double r41189 = r41186 / r41188;
        double r41190 = r41184 * r41189;
        double r41191 = r41184 * r41186;
        double r41192 = r41191 * r41188;
        double r41193 = r41190 + r41192;
        return r41193;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \cos re\right) \cdot e^{-im} + \left(0.5 \cdot \cos re\right) \cdot e^{im}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{\cos re}{e^{im}}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]

  5. Final simplification0.0

    \[\leadsto 0.5 \cdot \frac{\cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))