Average Error: 0.4 → 0.4
Time: 45.1s
Precision: 64
\[\frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]
↓
\[\frac{\frac{\left(\left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}\right) \cdot \left(\cos x \cdot \cos x - \cos y \cdot \cos y\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)}{\cos y + \cos x} + 2.0}{\left(\frac{\frac{3.0 \cdot 3.0 - 5.0}{\sqrt{5.0} + 3.0}}{2.0} \cdot \cos y + \left(\frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x + 1.0\right)\right) \cdot 3.0}\]
\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{\frac{\left(\left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}\right) \cdot \left(\cos x \cdot \cos x - \cos y \cdot \cos y\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)}{\cos y + \cos x} + 2.0}{\left(\frac{\frac{3.0 \cdot 3.0 - 5.0}{\sqrt{5.0} + 3.0}}{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 r9658402 = 2.0;
        double r9658403 = sqrt(r9658402);
        double r9658404 = x;
        double r9658405 = sin(r9658404);
        double r9658406 = y;
        double r9658407 = sin(r9658406);
        double r9658408 = 16.0;
        double r9658409 = r9658407 / r9658408;
        double r9658410 = r9658405 - r9658409;
        double r9658411 = r9658403 * r9658410;
        double r9658412 = r9658405 / r9658408;
        double r9658413 = r9658407 - r9658412;
        double r9658414 = r9658411 * r9658413;
        double r9658415 = cos(r9658404);
        double r9658416 = cos(r9658406);
        double r9658417 = r9658415 - r9658416;
        double r9658418 = r9658414 * r9658417;
        double r9658419 = r9658402 + r9658418;
        double r9658420 = 3.0;
        double r9658421 = 1.0;
        double r9658422 = 5.0;
        double r9658423 = sqrt(r9658422);
        double r9658424 = r9658423 - r9658421;
        double r9658425 = r9658424 / r9658402;
        double r9658426 = r9658425 * r9658415;
        double r9658427 = r9658421 + r9658426;
        double r9658428 = r9658420 - r9658423;
        double r9658429 = r9658428 / r9658402;
        double r9658430 = r9658429 * r9658416;
        double r9658431 = r9658427 + r9658430;
        double r9658432 = r9658420 * r9658431;
        double r9658433 = r9658419 / r9658432;
        return r9658433;
}
↓
double f(double x, double y) {
        double r9658434 = x;
        double r9658435 = sin(r9658434);
        double r9658436 = y;
        double r9658437 = sin(r9658436);
        double r9658438 = 16.0;
        double r9658439 = r9658437 / r9658438;
        double r9658440 = r9658435 - r9658439;
        double r9658441 = 2.0;
        double r9658442 = sqrt(r9658441);
        double r9658443 = r9658440 * r9658442;
        double r9658444 = cos(r9658434);
        double r9658445 = r9658444 * r9658444;
        double r9658446 = cos(r9658436);
        double r9658447 = r9658446 * r9658446;
        double r9658448 = r9658445 - r9658447;
        double r9658449 = r9658443 * r9658448;
        double r9658450 = r9658435 / r9658438;
        double r9658451 = r9658437 - r9658450;
        double r9658452 = r9658449 * r9658451;
        double r9658453 = r9658446 + r9658444;
        double r9658454 = r9658452 / r9658453;
        double r9658455 = r9658454 + r9658441;
        double r9658456 = 3.0;
        double r9658457 = r9658456 * r9658456;
        double r9658458 = 5.0;
        double r9658459 = r9658457 - r9658458;
        double r9658460 = sqrt(r9658458);
        double r9658461 = r9658460 + r9658456;
        double r9658462 = r9658459 / r9658461;
        double r9658463 = r9658462 / r9658441;
        double r9658464 = r9658463 * r9658446;
        double r9658465 = 1.0;
        double r9658466 = r9658460 - r9658465;
        double r9658467 = r9658466 / r9658441;
        double r9658468 = r9658467 * r9658444;
        double r9658469 = r9658468 + r9658465;
        double r9658470 = r9658464 + r9658469;
        double r9658471 = r9658470 * r9658456;
        double r9658472 = r9658455 / r9658471;
        return r9658472;
}

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 0.4

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

  3. Applied flip--0.5

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

  4. Simplified0.4

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

  6. Applied add-sqr-sqrt0.4

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

  7. Applied sqrt-prod0.4

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

  8. Applied associate-*l*0.4

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

  10. Applied flip--0.4

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

  11. Applied associate-*r/0.4

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

  12. Simplified0.4

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

  13. Final simplification0.4

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

Reproduce

herbie shell --seed 2019158 
(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))))))