Average Error: 0.5 → 0.4
Time: 41.0s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3}}{\left(1 + \frac{1}{\sqrt{2}} \cdot \left(\frac{\sqrt{5} - 1}{\sqrt{2}} \cdot \cos x\right)\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y}\]
\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{\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}}{\left(1 + \frac{1}{\sqrt{2}} \cdot \left(\frac{\sqrt{5} - 1}{\sqrt{2}} \cdot \cos x\right)\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y}
double f(double x, double y) {
        double r214431 = 2.0;
        double r214432 = sqrt(r214431);
        double r214433 = x;
        double r214434 = sin(r214433);
        double r214435 = y;
        double r214436 = sin(r214435);
        double r214437 = 16.0;
        double r214438 = r214436 / r214437;
        double r214439 = r214434 - r214438;
        double r214440 = r214432 * r214439;
        double r214441 = r214434 / r214437;
        double r214442 = r214436 - r214441;
        double r214443 = r214440 * r214442;
        double r214444 = cos(r214433);
        double r214445 = cos(r214435);
        double r214446 = r214444 - r214445;
        double r214447 = r214443 * r214446;
        double r214448 = r214431 + r214447;
        double r214449 = 3.0;
        double r214450 = 1.0;
        double r214451 = 5.0;
        double r214452 = sqrt(r214451);
        double r214453 = r214452 - r214450;
        double r214454 = r214453 / r214431;
        double r214455 = r214454 * r214444;
        double r214456 = r214450 + r214455;
        double r214457 = r214449 - r214452;
        double r214458 = r214457 / r214431;
        double r214459 = r214458 * r214445;
        double r214460 = r214456 + r214459;
        double r214461 = r214449 * r214460;
        double r214462 = r214448 / r214461;
        return r214462;
}
↓
double f(double x, double y) {
        double r214463 = 2.0;
        double r214464 = sqrt(r214463);
        double r214465 = x;
        double r214466 = sin(r214465);
        double r214467 = y;
        double r214468 = sin(r214467);
        double r214469 = 16.0;
        double r214470 = r214468 / r214469;
        double r214471 = r214466 - r214470;
        double r214472 = r214464 * r214471;
        double r214473 = r214466 / r214469;
        double r214474 = r214468 - r214473;
        double r214475 = r214472 * r214474;
        double r214476 = cos(r214465);
        double r214477 = cos(r214467);
        double r214478 = r214476 - r214477;
        double r214479 = r214475 * r214478;
        double r214480 = r214463 + r214479;
        double r214481 = 3.0;
        double r214482 = r214480 / r214481;
        double r214483 = 1.0;
        double r214484 = 1.0;
        double r214485 = r214484 / r214464;
        double r214486 = 5.0;
        double r214487 = sqrt(r214486);
        double r214488 = r214487 - r214483;
        double r214489 = r214488 / r214464;
        double r214490 = r214489 * r214476;
        double r214491 = r214485 * r214490;
        double r214492 = r214483 + r214491;
        double r214493 = r214481 * r214481;
        double r214494 = r214493 - r214486;
        double r214495 = r214481 + r214487;
        double r214496 = r214494 / r214495;
        double r214497 = r214496 / r214463;
        double r214498 = r214497 * r214477;
        double r214499 = r214492 + r214498;
        double r214500 = r214482 / r214499;
        return r214500;
}

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. Simplified0.5

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

  6. Applied add-sqr-sqrt0.5

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

  7. Applied *-un-lft-identity0.5

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

  8. Applied times-frac0.5

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

  9. Applied associate-*l*0.4

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

  11. Applied associate-/r*0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2019325 
(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))))))