Average Error: 0.0 → 0.0
Time: 15.4s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[e^{\log 0.5 - im} \cdot \cos re + \cos re \cdot \left(0.5 \cdot e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
e^{\log 0.5 - im} \cdot \cos re + \cos re \cdot \left(0.5 \cdot e^{im}\right)
double f(double re, double im) {
        double r918110 = 0.5;
        double r918111 = re;
        double r918112 = cos(r918111);
        double r918113 = r918110 * r918112;
        double r918114 = im;
        double r918115 = -r918114;
        double r918116 = exp(r918115);
        double r918117 = exp(r918114);
        double r918118 = r918116 + r918117;
        double r918119 = r918113 * r918118;
        return r918119;
}
↓
double f(double re, double im) {
        double r918120 = 0.5;
        double r918121 = log(r918120);
        double r918122 = im;
        double r918123 = r918121 - r918122;
        double r918124 = exp(r918123);
        double r918125 = re;
        double r918126 = cos(r918125);
        double r918127 = r918124 * r918126;
        double r918128 = exp(r918122);
        double r918129 = r918120 * r918128;
        double r918130 = r918126 * r918129;
        double r918131 = r918127 + r918130;
        return r918131;
}

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

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

  4. Applied distribute-lft-in0.0

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

  6. Applied add-exp-log0.0

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

  7. Applied div-exp0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))