Average Error: 0.5 → 0.5
Time: 33.4s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{1}{3} \cdot \frac{2 + \left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y}\]
\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{1}{3} \cdot \frac{2 + \left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y}
double f(double x, double y) {
        double r180464 = 2.0;
        double r180465 = sqrt(r180464);
        double r180466 = x;
        double r180467 = sin(r180466);
        double r180468 = y;
        double r180469 = sin(r180468);
        double r180470 = 16.0;
        double r180471 = r180469 / r180470;
        double r180472 = r180467 - r180471;
        double r180473 = r180465 * r180472;
        double r180474 = r180467 / r180470;
        double r180475 = r180469 - r180474;
        double r180476 = r180473 * r180475;
        double r180477 = cos(r180466);
        double r180478 = cos(r180468);
        double r180479 = r180477 - r180478;
        double r180480 = r180476 * r180479;
        double r180481 = r180464 + r180480;
        double r180482 = 3.0;
        double r180483 = 1.0;
        double r180484 = 5.0;
        double r180485 = sqrt(r180484);
        double r180486 = r180485 - r180483;
        double r180487 = r180486 / r180464;
        double r180488 = r180487 * r180477;
        double r180489 = r180483 + r180488;
        double r180490 = r180482 - r180485;
        double r180491 = r180490 / r180464;
        double r180492 = r180491 * r180478;
        double r180493 = r180489 + r180492;
        double r180494 = r180482 * r180493;
        double r180495 = r180481 / r180494;
        return r180495;
}
↓
double f(double x, double y) {
        double r180496 = 1.0;
        double r180497 = 3.0;
        double r180498 = r180496 / r180497;
        double r180499 = 2.0;
        double r180500 = sqrt(r180499);
        double r180501 = sqrt(r180500);
        double r180502 = x;
        double r180503 = sin(r180502);
        double r180504 = y;
        double r180505 = sin(r180504);
        double r180506 = 16.0;
        double r180507 = r180505 / r180506;
        double r180508 = r180503 - r180507;
        double r180509 = r180501 * r180508;
        double r180510 = r180501 * r180509;
        double r180511 = r180503 / r180506;
        double r180512 = r180505 - r180511;
        double r180513 = r180510 * r180512;
        double r180514 = cos(r180502);
        double r180515 = cos(r180504);
        double r180516 = r180514 - r180515;
        double r180517 = r180513 * r180516;
        double r180518 = r180499 + r180517;
        double r180519 = 1.0;
        double r180520 = 5.0;
        double r180521 = sqrt(r180520);
        double r180522 = r180521 - r180519;
        double r180523 = r180522 / r180499;
        double r180524 = r180523 * r180514;
        double r180525 = r180519 + r180524;
        double r180526 = r180497 - r180521;
        double r180527 = r180526 / r180499;
        double r180528 = r180527 * r180515;
        double r180529 = r180525 + r180528;
        double r180530 = r180518 / r180529;
        double r180531 = r180498 * r180530;
        return r180531;
}

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 *-un-lft-identity0.5

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

  4. Applied times-frac0.5

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

  6. Applied add-sqr-sqrt0.5

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

  7. Applied sqrt-prod0.5

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

  8. Applied associate-*l*0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2019208 
(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))))))