Average Error: 0.5 → 0.5
Time: 25.0s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \frac{\cos x \cdot \cos x - \cos y \cdot \cos y}{\cos x + \cos y}}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{\sqrt{5} + 3}}{2} \cdot \cos y\right)}\]
\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 - 5}{\sqrt{5} + 3}}{2} \cdot \cos y\right)}
double f(double x, double y) {
        double r237260 = 2.0;
        double r237261 = sqrt(r237260);
        double r237262 = x;
        double r237263 = sin(r237262);
        double r237264 = y;
        double r237265 = sin(r237264);
        double r237266 = 16.0;
        double r237267 = r237265 / r237266;
        double r237268 = r237263 - r237267;
        double r237269 = r237261 * r237268;
        double r237270 = r237263 / r237266;
        double r237271 = r237265 - r237270;
        double r237272 = r237269 * r237271;
        double r237273 = cos(r237262);
        double r237274 = cos(r237264);
        double r237275 = r237273 - r237274;
        double r237276 = r237272 * r237275;
        double r237277 = r237260 + r237276;
        double r237278 = 3.0;
        double r237279 = 1.0;
        double r237280 = 5.0;
        double r237281 = sqrt(r237280);
        double r237282 = r237281 - r237279;
        double r237283 = r237282 / r237260;
        double r237284 = r237283 * r237273;
        double r237285 = r237279 + r237284;
        double r237286 = r237278 - r237281;
        double r237287 = r237286 / r237260;
        double r237288 = r237287 * r237274;
        double r237289 = r237285 + r237288;
        double r237290 = r237278 * r237289;
        double r237291 = r237277 / r237290;
        return r237291;
}
↓
double f(double x, double y) {
        double r237292 = 2.0;
        double r237293 = sqrt(r237292);
        double r237294 = x;
        double r237295 = sin(r237294);
        double r237296 = y;
        double r237297 = sin(r237296);
        double r237298 = 16.0;
        double r237299 = r237297 / r237298;
        double r237300 = r237295 - r237299;
        double r237301 = r237293 * r237300;
        double r237302 = r237295 / r237298;
        double r237303 = r237297 - r237302;
        double r237304 = r237301 * r237303;
        double r237305 = cos(r237294);
        double r237306 = r237305 * r237305;
        double r237307 = cos(r237296);
        double r237308 = r237307 * r237307;
        double r237309 = r237306 - r237308;
        double r237310 = r237305 + r237307;
        double r237311 = r237309 / r237310;
        double r237312 = r237304 * r237311;
        double r237313 = r237292 + r237312;
        double r237314 = 3.0;
        double r237315 = 1.0;
        double r237316 = 5.0;
        double r237317 = sqrt(r237316);
        double r237318 = r237317 - r237315;
        double r237319 = r237318 / r237292;
        double r237320 = r237319 * r237305;
        double r237321 = r237315 + r237320;
        double r237322 = r237314 * r237314;
        double r237323 = r237322 - r237316;
        double r237324 = r237317 + r237314;
        double r237325 = r237323 / r237324;
        double r237326 = r237325 / r237292;
        double r237327 = r237326 * r237307;
        double r237328 = r237321 + r237327;
        double r237329 = r237314 * r237328;
        double r237330 = r237313 / r237329;
        return r237330;
}

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

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

  5. Applied flip--0.5

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

  6. Simplified0.5

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

  7. Simplified0.5

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

  8. Final simplification0.5

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(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))))))