Average Error: 0.0 → 0.0
Time: 16.5s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}
double f(double re, double im) {
        double r29168 = 0.5;
        double r29169 = re;
        double r29170 = cos(r29169);
        double r29171 = r29168 * r29170;
        double r29172 = im;
        double r29173 = -r29172;
        double r29174 = exp(r29173);
        double r29175 = exp(r29172);
        double r29176 = r29174 + r29175;
        double r29177 = r29171 * r29176;
        return r29177;
}
↓
double f(double re, double im) {
        double r29178 = 0.5;
        double r29179 = re;
        double r29180 = cos(r29179);
        double r29181 = r29178 * r29180;
        double r29182 = im;
        double r29183 = exp(r29182);
        double r29184 = r29181 / r29183;
        double r29185 = r29181 * r29183;
        double r29186 = r29184 + r29185;
        return r29186;
}

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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))