Average Error: 0.5 → 0.5
Time: 10.5s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \frac{\cos x \cdot \cos x - \cos y \cdot \cos y}{\cos x + \cos y}}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 + \left(-5\right)}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
\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(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \frac{\cos x \cdot \cos x - \cos y \cdot \cos y}{\cos x + \cos y}}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 + \left(-5\right)}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}
double f(double x, double y) {
        double r199483 = 2.0;
        double r199484 = sqrt(r199483);
        double r199485 = x;
        double r199486 = sin(r199485);
        double r199487 = y;
        double r199488 = sin(r199487);
        double r199489 = 16.0;
        double r199490 = r199488 / r199489;
        double r199491 = r199486 - r199490;
        double r199492 = r199484 * r199491;
        double r199493 = r199486 / r199489;
        double r199494 = r199488 - r199493;
        double r199495 = r199492 * r199494;
        double r199496 = cos(r199485);
        double r199497 = cos(r199487);
        double r199498 = r199496 - r199497;
        double r199499 = r199495 * r199498;
        double r199500 = r199483 + r199499;
        double r199501 = 3.0;
        double r199502 = 1.0;
        double r199503 = 5.0;
        double r199504 = sqrt(r199503);
        double r199505 = r199504 - r199502;
        double r199506 = r199505 / r199483;
        double r199507 = r199506 * r199496;
        double r199508 = r199502 + r199507;
        double r199509 = r199501 - r199504;
        double r199510 = r199509 / r199483;
        double r199511 = r199510 * r199497;
        double r199512 = r199508 + r199511;
        double r199513 = r199501 * r199512;
        double r199514 = r199500 / r199513;
        return r199514;
}
↓
double f(double x, double y) {
        double r199515 = 2.0;
        double r199516 = sqrt(r199515);
        double r199517 = x;
        double r199518 = sin(r199517);
        double r199519 = y;
        double r199520 = sin(r199519);
        double r199521 = 16.0;
        double r199522 = r199520 / r199521;
        double r199523 = r199518 - r199522;
        double r199524 = r199516 * r199523;
        double r199525 = r199518 / r199521;
        double r199526 = r199520 - r199525;
        double r199527 = r199524 * r199526;
        double r199528 = cos(r199517);
        double r199529 = r199528 * r199528;
        double r199530 = cos(r199519);
        double r199531 = r199530 * r199530;
        double r199532 = r199529 - r199531;
        double r199533 = r199528 + r199530;
        double r199534 = r199532 / r199533;
        double r199535 = r199527 * r199534;
        double r199536 = r199515 + r199535;
        double r199537 = 3.0;
        double r199538 = 1.0;
        double r199539 = 5.0;
        double r199540 = sqrt(r199539);
        double r199541 = r199540 - r199538;
        double r199542 = r199541 / r199515;
        double r199543 = r199542 * r199528;
        double r199544 = r199538 + r199543;
        double r199545 = r199537 * r199537;
        double r199546 = -r199539;
        double r199547 = r199545 + r199546;
        double r199548 = r199537 + r199540;
        double r199549 = r199547 / r199548;
        double r199550 = r199549 / r199515;
        double r199551 = r199550 * r199530;
        double r199552 = r199544 + r199551;
        double r199553 = r199537 * r199552;
        double r199554 = r199536 / r199553;
        return r199554;
}

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

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

  6. Applied flip--0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2020062 
(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))))))