Average Error: 0.0 → 0.0
Time: 4.2s
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 r97073 = 0.5;
        double r97074 = re;
        double r97075 = cos(r97074);
        double r97076 = r97073 * r97075;
        double r97077 = im;
        double r97078 = -r97077;
        double r97079 = exp(r97078);
        double r97080 = exp(r97077);
        double r97081 = r97079 + r97080;
        double r97082 = r97076 * r97081;
        return r97082;
}
↓
double f(double re, double im) {
        double r97083 = 0.5;
        double r97084 = re;
        double r97085 = cos(r97084);
        double r97086 = r97083 * r97085;
        double r97087 = im;
        double r97088 = exp(r97087);
        double r97089 = r97086 / r97088;
        double r97090 = r97086 * r97088;
        double r97091 = r97089 + r97090;
        return r97091;
}

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 2020049 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))