Average Error: 0.5 → 0.5
Time: 43.8s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{\left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right) + 2}{\left(\cos y \cdot \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + 1\right)\right) \cdot 3}\]
\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{\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) + 2}{\left(\cos y \cdot \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + 1\right)\right) \cdot 3}
double f(double x, double y) {
        double r9722502 = 2.0;
        double r9722503 = sqrt(r9722502);
        double r9722504 = x;
        double r9722505 = sin(r9722504);
        double r9722506 = y;
        double r9722507 = sin(r9722506);
        double r9722508 = 16.0;
        double r9722509 = r9722507 / r9722508;
        double r9722510 = r9722505 - r9722509;
        double r9722511 = r9722503 * r9722510;
        double r9722512 = r9722505 / r9722508;
        double r9722513 = r9722507 - r9722512;
        double r9722514 = r9722511 * r9722513;
        double r9722515 = cos(r9722504);
        double r9722516 = cos(r9722506);
        double r9722517 = r9722515 - r9722516;
        double r9722518 = r9722514 * r9722517;
        double r9722519 = r9722502 + r9722518;
        double r9722520 = 3.0;
        double r9722521 = 1.0;
        double r9722522 = 5.0;
        double r9722523 = sqrt(r9722522);
        double r9722524 = r9722523 - r9722521;
        double r9722525 = r9722524 / r9722502;
        double r9722526 = r9722525 * r9722515;
        double r9722527 = r9722521 + r9722526;
        double r9722528 = r9722520 - r9722523;
        double r9722529 = r9722528 / r9722502;
        double r9722530 = r9722529 * r9722516;
        double r9722531 = r9722527 + r9722530;
        double r9722532 = r9722520 * r9722531;
        double r9722533 = r9722519 / r9722532;
        return r9722533;
}
↓
double f(double x, double y) {
        double r9722534 = 2.0;
        double r9722535 = sqrt(r9722534);
        double r9722536 = sqrt(r9722535);
        double r9722537 = x;
        double r9722538 = sin(r9722537);
        double r9722539 = y;
        double r9722540 = sin(r9722539);
        double r9722541 = 16.0;
        double r9722542 = r9722540 / r9722541;
        double r9722543 = r9722538 - r9722542;
        double r9722544 = r9722536 * r9722543;
        double r9722545 = r9722536 * r9722544;
        double r9722546 = r9722538 / r9722541;
        double r9722547 = r9722540 - r9722546;
        double r9722548 = r9722545 * r9722547;
        double r9722549 = cos(r9722537);
        double r9722550 = cos(r9722539);
        double r9722551 = r9722549 - r9722550;
        double r9722552 = r9722548 * r9722551;
        double r9722553 = r9722552 + r9722534;
        double r9722554 = 3.0;
        double r9722555 = r9722554 * r9722554;
        double r9722556 = 5.0;
        double r9722557 = r9722555 - r9722556;
        double r9722558 = sqrt(r9722556);
        double r9722559 = r9722554 + r9722558;
        double r9722560 = r9722557 / r9722559;
        double r9722561 = r9722560 / r9722534;
        double r9722562 = r9722550 * r9722561;
        double r9722563 = 1.0;
        double r9722564 = r9722558 - r9722563;
        double r9722565 = r9722564 / r9722534;
        double r9722566 = r9722549 * r9722565;
        double r9722567 = r9722566 + r9722563;
        double r9722568 = r9722562 + r9722567;
        double r9722569 = r9722568 * r9722554;
        double r9722570 = r9722553 / r9722569;
        return r9722570;
}

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 add-sqr-sqrt0.5

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

  4. Applied sqrt-prod0.5

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

  5. Applied associate-*l*0.5

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

  7. Applied flip--0.5

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

  8. Simplified0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2019174 
(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))))))