Average Error: 0.5 → 0.5
Time: 44.0s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\left(\left(\sqrt[3]{\sin x - \frac{\sin y}{16}} \cdot \sqrt[3]{\sin x - \frac{\sin y}{16}}\right) \cdot \sqrt{2}\right) \cdot \sqrt[3]{\sin x - \frac{\sin y}{16}}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
\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 \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(\left(\left(\sqrt[3]{\sin x - \frac{\sin y}{16}} \cdot \sqrt[3]{\sin x - \frac{\sin y}{16}}\right) \cdot \sqrt{2}\right) \cdot \sqrt[3]{\sin x - \frac{\sin y}{16}}\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)}
double f(double x, double y) {
        double r191493 = 2.0;
        double r191494 = sqrt(r191493);
        double r191495 = x;
        double r191496 = sin(r191495);
        double r191497 = y;
        double r191498 = sin(r191497);
        double r191499 = 16.0;
        double r191500 = r191498 / r191499;
        double r191501 = r191496 - r191500;
        double r191502 = r191494 * r191501;
        double r191503 = r191496 / r191499;
        double r191504 = r191498 - r191503;
        double r191505 = r191502 * r191504;
        double r191506 = cos(r191495);
        double r191507 = cos(r191497);
        double r191508 = r191506 - r191507;
        double r191509 = r191505 * r191508;
        double r191510 = r191493 + r191509;
        double r191511 = 3.0;
        double r191512 = 1.0;
        double r191513 = 5.0;
        double r191514 = sqrt(r191513);
        double r191515 = r191514 - r191512;
        double r191516 = r191515 / r191493;
        double r191517 = r191516 * r191506;
        double r191518 = r191512 + r191517;
        double r191519 = r191511 - r191514;
        double r191520 = r191519 / r191493;
        double r191521 = r191520 * r191507;
        double r191522 = r191518 + r191521;
        double r191523 = r191511 * r191522;
        double r191524 = r191510 / r191523;
        return r191524;
}
↓
double f(double x, double y) {
        double r191525 = 2.0;
        double r191526 = x;
        double r191527 = sin(r191526);
        double r191528 = y;
        double r191529 = sin(r191528);
        double r191530 = 16.0;
        double r191531 = r191529 / r191530;
        double r191532 = r191527 - r191531;
        double r191533 = cbrt(r191532);
        double r191534 = r191533 * r191533;
        double r191535 = sqrt(r191525);
        double r191536 = r191534 * r191535;
        double r191537 = r191536 * r191533;
        double r191538 = r191527 / r191530;
        double r191539 = r191529 - r191538;
        double r191540 = r191537 * r191539;
        double r191541 = cos(r191526);
        double r191542 = cos(r191528);
        double r191543 = r191541 - r191542;
        double r191544 = r191540 * r191543;
        double r191545 = r191525 + r191544;
        double r191546 = 3.0;
        double r191547 = 1.0;
        double r191548 = 5.0;
        double r191549 = sqrt(r191548);
        double r191550 = r191549 - r191547;
        double r191551 = r191550 / r191525;
        double r191552 = r191551 * r191541;
        double r191553 = r191547 + r191552;
        double r191554 = r191546 - r191549;
        double r191555 = r191554 / r191525;
        double r191556 = r191555 * r191542;
        double r191557 = r191553 + r191556;
        double r191558 = r191546 * r191557;
        double r191559 = r191545 / r191558;
        return r191559;
}

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-cube-cbrt0.5

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

  4. Applied associate-*r*0.5

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

  5. Simplified0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019199 
(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))))))