Average Error: 0.5 → 0.5
Time: 48.1s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \sqrt[3]{\left({\left(\sin x - \frac{\sin y}{16}\right)}^{3} \cdot \left(2 \cdot \sqrt{2}\right)\right) \cdot {\left(\sin y - \frac{\sin x}{16}\right)}^{3}} \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}
↓
\frac{2 + \sqrt[3]{\left({\left(\sin x - \frac{\sin y}{16}\right)}^{3} \cdot \left(2 \cdot \sqrt{2}\right)\right) \cdot {\left(\sin y - \frac{\sin x}{16}\right)}^{3}} \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}
double f(double x, double y) {
        double r161306 = 2.0;
        double r161307 = sqrt(r161306);
        double r161308 = x;
        double r161309 = sin(r161308);
        double r161310 = y;
        double r161311 = sin(r161310);
        double r161312 = 16.0;
        double r161313 = r161311 / r161312;
        double r161314 = r161309 - r161313;
        double r161315 = r161307 * r161314;
        double r161316 = r161309 / r161312;
        double r161317 = r161311 - r161316;
        double r161318 = r161315 * r161317;
        double r161319 = cos(r161308);
        double r161320 = cos(r161310);
        double r161321 = r161319 - r161320;
        double r161322 = r161318 * r161321;
        double r161323 = r161306 + r161322;
        double r161324 = 3.0;
        double r161325 = 1.0;
        double r161326 = 5.0;
        double r161327 = sqrt(r161326);
        double r161328 = r161327 - r161325;
        double r161329 = r161328 / r161306;
        double r161330 = r161329 * r161319;
        double r161331 = r161325 + r161330;
        double r161332 = r161324 - r161327;
        double r161333 = r161332 / r161306;
        double r161334 = r161333 * r161320;
        double r161335 = r161331 + r161334;
        double r161336 = r161324 * r161335;
        double r161337 = r161323 / r161336;
        return r161337;
}
↓
double f(double x, double y) {
        double r161338 = 2.0;
        double r161339 = x;
        double r161340 = sin(r161339);
        double r161341 = y;
        double r161342 = sin(r161341);
        double r161343 = 16.0;
        double r161344 = r161342 / r161343;
        double r161345 = r161340 - r161344;
        double r161346 = 3.0;
        double r161347 = pow(r161345, r161346);
        double r161348 = sqrt(r161338);
        double r161349 = r161338 * r161348;
        double r161350 = r161347 * r161349;
        double r161351 = r161340 / r161343;
        double r161352 = r161342 - r161351;
        double r161353 = pow(r161352, r161346);
        double r161354 = r161350 * r161353;
        double r161355 = cbrt(r161354);
        double r161356 = cos(r161339);
        double r161357 = cos(r161341);
        double r161358 = r161356 - r161357;
        double r161359 = r161355 * r161358;
        double r161360 = r161338 + r161359;
        double r161361 = 3.0;
        double r161362 = 1.0;
        double r161363 = 5.0;
        double r161364 = sqrt(r161363);
        double r161365 = r161364 - r161362;
        double r161366 = r161365 / r161338;
        double r161367 = r161366 * r161356;
        double r161368 = r161362 + r161367;
        double r161369 = r161361 - r161364;
        double r161370 = r161369 / r161338;
        double r161371 = r161370 * r161357;
        double r161372 = r161368 + r161371;
        double r161373 = r161361 * r161372;
        double r161374 = r161360 / r161373;
        return r161374;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \color{blue}{\sqrt[3]{\left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}}\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]

  4. Applied add-cbrt-cube0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \color{blue}{\sqrt[3]{\left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin x - \frac{\sin y}{16}\right)}}\right) \cdot \sqrt[3]{\left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]

  5. Applied add-cbrt-cube0.5

    \[\leadsto \frac{2 + \left(\left(\color{blue}{\sqrt[3]{\left(\sqrt{2} \cdot \sqrt{2}\right) \cdot \sqrt{2}}} \cdot \sqrt[3]{\left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin x - \frac{\sin y}{16}\right)}\right) \cdot \sqrt[3]{\left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]

  6. Applied cbrt-unprod0.5

    \[\leadsto \frac{2 + \left(\color{blue}{\sqrt[3]{\left(\left(\sqrt{2} \cdot \sqrt{2}\right) \cdot \sqrt{2}\right) \cdot \left(\left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)}} \cdot \sqrt[3]{\left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]

  7. Applied cbrt-unprod0.5

    \[\leadsto \frac{2 + \color{blue}{\sqrt[3]{\left(\left(\left(\sqrt{2} \cdot \sqrt{2}\right) \cdot \sqrt{2}\right) \cdot \left(\left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}} \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]

  8. Simplified0.5

    \[\leadsto \frac{2 + \sqrt[3]{\color{blue}{\left({\left(\sin x - \frac{\sin y}{16}\right)}^{3} \cdot \left(2 \cdot \sqrt{2}\right)\right) \cdot {\left(\sin y - \frac{\sin x}{16}\right)}^{3}}} \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]

  9. Final simplification0.5

    \[\leadsto \frac{2 + \sqrt[3]{\left({\left(\sin x - \frac{\sin y}{16}\right)}^{3} \cdot \left(2 \cdot \sqrt{2}\right)\right) \cdot {\left(\sin y - \frac{\sin x}{16}\right)}^{3}} \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5"
  (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y))))))