Average Error: 0.5 → 0.5
Time: 31.7s
Precision: 64
\[\frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]
↓
\[\frac{\left(\left(\left(\sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}} \cdot \sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}}\right) \cdot \left(\log \left(\sqrt{e^{\sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}}}}\right) + \log \left(\sqrt{e^{\sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}}}}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right) + 2.0}{\left(\frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y + \left(\frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x + 1.0\right)\right) \cdot 3.0}\]
\frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}
↓
\frac{\left(\left(\left(\sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}} \cdot \sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}}\right) \cdot \left(\log \left(\sqrt{e^{\sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}}}}\right) + \log \left(\sqrt{e^{\sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}}}}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right) + 2.0}{\left(\frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y + \left(\frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x + 1.0\right)\right) \cdot 3.0}
double f(double x, double y) {
        double r4796311 = 2.0;
        double r4796312 = sqrt(r4796311);
        double r4796313 = x;
        double r4796314 = sin(r4796313);
        double r4796315 = y;
        double r4796316 = sin(r4796315);
        double r4796317 = 16.0;
        double r4796318 = r4796316 / r4796317;
        double r4796319 = r4796314 - r4796318;
        double r4796320 = r4796312 * r4796319;
        double r4796321 = r4796314 / r4796317;
        double r4796322 = r4796316 - r4796321;
        double r4796323 = r4796320 * r4796322;
        double r4796324 = cos(r4796313);
        double r4796325 = cos(r4796315);
        double r4796326 = r4796324 - r4796325;
        double r4796327 = r4796323 * r4796326;
        double r4796328 = r4796311 + r4796327;
        double r4796329 = 3.0;
        double r4796330 = 1.0;
        double r4796331 = 5.0;
        double r4796332 = sqrt(r4796331);
        double r4796333 = r4796332 - r4796330;
        double r4796334 = r4796333 / r4796311;
        double r4796335 = r4796334 * r4796324;
        double r4796336 = r4796330 + r4796335;
        double r4796337 = r4796329 - r4796332;
        double r4796338 = r4796337 / r4796311;
        double r4796339 = r4796338 * r4796325;
        double r4796340 = r4796336 + r4796339;
        double r4796341 = r4796329 * r4796340;
        double r4796342 = r4796328 / r4796341;
        return r4796342;
}
↓
double f(double x, double y) {
        double r4796343 = x;
        double r4796344 = sin(r4796343);
        double r4796345 = y;
        double r4796346 = sin(r4796345);
        double r4796347 = 16.0;
        double r4796348 = r4796346 / r4796347;
        double r4796349 = r4796344 - r4796348;
        double r4796350 = 2.0;
        double r4796351 = sqrt(r4796350);
        double r4796352 = r4796349 * r4796351;
        double r4796353 = cbrt(r4796352);
        double r4796354 = r4796353 * r4796353;
        double r4796355 = exp(r4796353);
        double r4796356 = sqrt(r4796355);
        double r4796357 = log(r4796356);
        double r4796358 = r4796357 + r4796357;
        double r4796359 = r4796354 * r4796358;
        double r4796360 = r4796344 / r4796347;
        double r4796361 = r4796346 - r4796360;
        double r4796362 = r4796359 * r4796361;
        double r4796363 = cos(r4796343);
        double r4796364 = cos(r4796345);
        double r4796365 = r4796363 - r4796364;
        double r4796366 = r4796362 * r4796365;
        double r4796367 = r4796366 + r4796350;
        double r4796368 = 3.0;
        double r4796369 = 5.0;
        double r4796370 = sqrt(r4796369);
        double r4796371 = r4796368 - r4796370;
        double r4796372 = r4796371 / r4796350;
        double r4796373 = r4796372 * r4796364;
        double r4796374 = 1.0;
        double r4796375 = r4796370 - r4796374;
        double r4796376 = r4796375 / r4796350;
        double r4796377 = r4796376 * r4796363;
        double r4796378 = r4796377 + r4796374;
        double r4796379 = r4796373 + r4796378;
        double r4796380 = r4796379 * r4796368;
        double r4796381 = r4796367 / r4796380;
        return r4796381;
}

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

    \[\frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.5

    \[\leadsto \frac{2.0 + \left(\color{blue}{\left(\left(\sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)} \cdot \sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}\right) \cdot \sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}\right)} \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]
  4. Using strategy rm

  5. Applied add-log-exp0.5

    \[\leadsto \frac{2.0 + \left(\left(\left(\sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)} \cdot \sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}\right) \cdot \color{blue}{\log \left(e^{\sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}}\right)}\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt0.5

    \[\leadsto \frac{2.0 + \left(\left(\left(\sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)} \cdot \sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}\right) \cdot \log \color{blue}{\left(\sqrt{e^{\sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}}} \cdot \sqrt{e^{\sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}}}\right)}\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]

  8. Applied log-prod0.5

    \[\leadsto \frac{2.0 + \left(\left(\left(\sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)} \cdot \sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}\right) \cdot \color{blue}{\left(\log \left(\sqrt{e^{\sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}}}\right) + \log \left(\sqrt{e^{\sqrt[3]{\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}}}\right)\right)}\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]

  9. Final simplification0.5

    \[\leadsto \frac{\left(\left(\left(\sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}} \cdot \sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}}\right) \cdot \left(\log \left(\sqrt{e^{\sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}}}}\right) + \log \left(\sqrt{e^{\sqrt[3]{\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}}}}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right) + 2.0}{\left(\frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y + \left(\frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x + 1.0\right)\right) \cdot 3.0}\]

Reproduce

herbie shell --seed 2019156 
(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))))))