Average Error: 0.5 → 0.5
Time: 17.5s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\sqrt[3]{\log \left(e^{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right)} \cdot \sqrt[3]{\log \left(e^{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right)}\right) \cdot \left(\sqrt[3]{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)} \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
\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 + \left(\sqrt[3]{\log \left(e^{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right)} \cdot \sqrt[3]{\log \left(e^{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right)}\right) \cdot \left(\sqrt[3]{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)} \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}
double f(double x, double y) {
        double r224302 = 2.0;
        double r224303 = sqrt(r224302);
        double r224304 = x;
        double r224305 = sin(r224304);
        double r224306 = y;
        double r224307 = sin(r224306);
        double r224308 = 16.0;
        double r224309 = r224307 / r224308;
        double r224310 = r224305 - r224309;
        double r224311 = r224303 * r224310;
        double r224312 = r224305 / r224308;
        double r224313 = r224307 - r224312;
        double r224314 = r224311 * r224313;
        double r224315 = cos(r224304);
        double r224316 = cos(r224306);
        double r224317 = r224315 - r224316;
        double r224318 = r224314 * r224317;
        double r224319 = r224302 + r224318;
        double r224320 = 3.0;
        double r224321 = 1.0;
        double r224322 = 5.0;
        double r224323 = sqrt(r224322);
        double r224324 = r224323 - r224321;
        double r224325 = r224324 / r224302;
        double r224326 = r224325 * r224315;
        double r224327 = r224321 + r224326;
        double r224328 = r224320 - r224323;
        double r224329 = r224328 / r224302;
        double r224330 = r224329 * r224316;
        double r224331 = r224327 + r224330;
        double r224332 = r224320 * r224331;
        double r224333 = r224319 / r224332;
        return r224333;
}
↓
double f(double x, double y) {
        double r224334 = 2.0;
        double r224335 = sqrt(r224334);
        double r224336 = x;
        double r224337 = sin(r224336);
        double r224338 = y;
        double r224339 = sin(r224338);
        double r224340 = 16.0;
        double r224341 = r224339 / r224340;
        double r224342 = r224337 - r224341;
        double r224343 = r224335 * r224342;
        double r224344 = r224337 / r224340;
        double r224345 = r224339 - r224344;
        double r224346 = r224343 * r224345;
        double r224347 = exp(r224346);
        double r224348 = log(r224347);
        double r224349 = cbrt(r224348);
        double r224350 = r224349 * r224349;
        double r224351 = cbrt(r224346);
        double r224352 = cos(r224336);
        double r224353 = cos(r224338);
        double r224354 = r224352 - r224353;
        double r224355 = r224351 * r224354;
        double r224356 = r224350 * r224355;
        double r224357 = r224334 + r224356;
        double r224358 = 3.0;
        double r224359 = 1.0;
        double r224360 = 5.0;
        double r224361 = sqrt(r224360);
        double r224362 = r224361 - r224359;
        double r224363 = r224362 / r224334;
        double r224364 = r224363 * r224352;
        double r224365 = r224359 + r224364;
        double r224366 = r224358 * r224358;
        double r224367 = r224366 - r224360;
        double r224368 = r224358 + r224361;
        double r224369 = r224367 / r224368;
        double r224370 = r224369 / r224334;
        double r224371 = r224370 * r224353;
        double r224372 = r224365 + r224371;
        double r224373 = r224358 * r224372;
        double r224374 = r224357 / r224373;
        return r224374;
}

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 flip--0.5

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

  4. Simplified0.4

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

  6. Applied add-log-exp0.4

    \[\leadsto \frac{2 + \color{blue}{\log \left(e^{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right)} \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.5

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

  9. Applied associate-*l*0.5

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

  10. Simplified0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y)
  :name "Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5"
  :precision binary64
  (/ (+ 2 (* (* (* (sqrt 2) (- (sin x) (/ (sin y) 16))) (- (sin y) (/ (sin x) 16))) (- (cos x) (cos y)))) (* 3 (+ (+ 1 (* (/ (- (sqrt 5) 1) 2) (cos x))) (* (/ (- 3 (sqrt 5)) 2) (cos y))))))