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 r38148 = 0.5;
        double r38149 = re;
        double r38150 = cos(r38149);
        double r38151 = r38148 * r38150;
        double r38152 = im;
        double r38153 = -r38152;
        double r38154 = exp(r38153);
        double r38155 = exp(r38152);
        double r38156 = r38154 + r38155;
        double r38157 = r38151 * r38156;
        return r38157;
}
↓
double f(double re, double im) {
        double r38158 = 0.5;
        double r38159 = re;
        double r38160 = cos(r38159);
        double r38161 = r38158 * r38160;
        double r38162 = im;
        double r38163 = exp(r38162);
        double r38164 = r38161 / r38163;
        double r38165 = r38161 * r38163;
        double r38166 = r38164 + r38165;
        return r38166;
}

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 2020034 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))