Average Error: 0.5 → 0.5
Time: 10.8s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\sqrt[3]{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)} \cdot \sqrt[3]{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right) \cdot \sqrt[3]{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
\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 \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[3]{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)} \cdot \sqrt[3]{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right) \cdot \sqrt[3]{\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)}
double f(double x, double y) {
        double r180359 = 2.0;
        double r180360 = sqrt(r180359);
        double r180361 = x;
        double r180362 = sin(r180361);
        double r180363 = y;
        double r180364 = sin(r180363);
        double r180365 = 16.0;
        double r180366 = r180364 / r180365;
        double r180367 = r180362 - r180366;
        double r180368 = r180360 * r180367;
        double r180369 = r180362 / r180365;
        double r180370 = r180364 - r180369;
        double r180371 = r180368 * r180370;
        double r180372 = cos(r180361);
        double r180373 = cos(r180363);
        double r180374 = r180372 - r180373;
        double r180375 = r180371 * r180374;
        double r180376 = r180359 + r180375;
        double r180377 = 3.0;
        double r180378 = 1.0;
        double r180379 = 5.0;
        double r180380 = sqrt(r180379);
        double r180381 = r180380 - r180378;
        double r180382 = r180381 / r180359;
        double r180383 = r180382 * r180372;
        double r180384 = r180378 + r180383;
        double r180385 = r180377 - r180380;
        double r180386 = r180385 / r180359;
        double r180387 = r180386 * r180373;
        double r180388 = r180384 + r180387;
        double r180389 = r180377 * r180388;
        double r180390 = r180376 / r180389;
        return r180390;
}
↓
double f(double x, double y) {
        double r180391 = 2.0;
        double r180392 = sqrt(r180391);
        double r180393 = x;
        double r180394 = sin(r180393);
        double r180395 = y;
        double r180396 = sin(r180395);
        double r180397 = 16.0;
        double r180398 = r180396 / r180397;
        double r180399 = r180394 - r180398;
        double r180400 = r180392 * r180399;
        double r180401 = r180394 / r180397;
        double r180402 = r180396 - r180401;
        double r180403 = r180400 * r180402;
        double r180404 = cbrt(r180403);
        double r180405 = r180404 * r180404;
        double r180406 = r180405 * r180404;
        double r180407 = cos(r180393);
        double r180408 = cos(r180395);
        double r180409 = r180407 - r180408;
        double r180410 = r180406 * r180409;
        double r180411 = r180391 + r180410;
        double r180412 = 3.0;
        double r180413 = 1.0;
        double r180414 = 5.0;
        double r180415 = sqrt(r180414);
        double r180416 = r180415 - r180413;
        double r180417 = r180416 / r180391;
        double r180418 = r180417 * r180407;
        double r180419 = r180413 + r180418;
        double r180420 = r180412 - r180415;
        double r180421 = r180420 / r180391;
        double r180422 = r180421 * r180408;
        double r180423 = r180419 + r180422;
        double r180424 = r180412 * r180423;
        double r180425 = r180411 / r180424;
        return r180425;
}

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

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020060 
(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))))))