Average Error: 0.0 → 0.0
Time: 20.6s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(\frac{\frac{0.5}{\sqrt{e^{im}}}}{\sqrt{e^{im}}} + 0.5 \cdot e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(\frac{\frac{0.5}{\sqrt{e^{im}}}}{\sqrt{e^{im}}} + 0.5 \cdot e^{im}\right)
double f(double re, double im) {
        double r1037139 = 0.5;
        double r1037140 = re;
        double r1037141 = cos(r1037140);
        double r1037142 = r1037139 * r1037141;
        double r1037143 = im;
        double r1037144 = -r1037143;
        double r1037145 = exp(r1037144);
        double r1037146 = exp(r1037143);
        double r1037147 = r1037145 + r1037146;
        double r1037148 = r1037142 * r1037147;
        return r1037148;
}
↓
double f(double re, double im) {
        double r1037149 = re;
        double r1037150 = cos(r1037149);
        double r1037151 = 0.5;
        double r1037152 = im;
        double r1037153 = exp(r1037152);
        double r1037154 = sqrt(r1037153);
        double r1037155 = r1037151 / r1037154;
        double r1037156 = r1037155 / r1037154;
        double r1037157 = r1037151 * r1037153;
        double r1037158 = r1037156 + r1037157;
        double r1037159 = r1037150 * r1037158;
        return r1037159;
}

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. Simplified0.0

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied associate-/r*0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))