Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{\frac{0.5 \cdot \cos re}{\sqrt{e^{im}}}}{\sqrt{e^{im}}} + \sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \cos re\right)\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{\frac{0.5 \cdot \cos re}{\sqrt{e^{im}}}}{\sqrt{e^{im}}} + \sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \cos re\right)\right)
double f(double re, double im) {
        double r104268 = 0.5;
        double r104269 = re;
        double r104270 = cos(r104269);
        double r104271 = r104268 * r104270;
        double r104272 = im;
        double r104273 = -r104272;
        double r104274 = exp(r104273);
        double r104275 = exp(r104272);
        double r104276 = r104274 + r104275;
        double r104277 = r104271 * r104276;
        return r104277;
}
↓
double f(double re, double im) {
        double r104278 = 0.5;
        double r104279 = re;
        double r104280 = cos(r104279);
        double r104281 = r104278 * r104280;
        double r104282 = im;
        double r104283 = exp(r104282);
        double r104284 = sqrt(r104283);
        double r104285 = r104281 / r104284;
        double r104286 = r104285 / r104284;
        double r104287 = r104284 * r104281;
        double r104288 = r104284 * r104287;
        double r104289 = r104286 + r104288;
        return r104289;
}

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. Simplified0.0

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

  7. Applied add-sqr-sqrt0.0

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

  8. Applied associate-/r*0.0

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

  10. Applied add-sqr-sqrt0.0

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

  11. Applied associate-*l*0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))