Average Error: 0.5 → 0.5
Time: 39.3s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \sqrt[3]{\cos x - \cos y}\right)\right)\right)}{3 \cdot \left(\frac{\frac{{3}^{3} - \sqrt{5} \cdot 5}{3 \cdot \left(3 + \sqrt{5}\right) + 5}}{2} \cdot \cos y + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + 1\right)\right)}\]
\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(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \sqrt[3]{\cos x - \cos y}\right)\right)\right)}{3 \cdot \left(\frac{\frac{{3}^{3} - \sqrt{5} \cdot 5}{3 \cdot \left(3 + \sqrt{5}\right) + 5}}{2} \cdot \cos y + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + 1\right)\right)}
double f(double x, double y) {
        double r162218 = 2.0;
        double r162219 = sqrt(r162218);
        double r162220 = x;
        double r162221 = sin(r162220);
        double r162222 = y;
        double r162223 = sin(r162222);
        double r162224 = 16.0;
        double r162225 = r162223 / r162224;
        double r162226 = r162221 - r162225;
        double r162227 = r162219 * r162226;
        double r162228 = r162221 / r162224;
        double r162229 = r162223 - r162228;
        double r162230 = r162227 * r162229;
        double r162231 = cos(r162220);
        double r162232 = cos(r162222);
        double r162233 = r162231 - r162232;
        double r162234 = r162230 * r162233;
        double r162235 = r162218 + r162234;
        double r162236 = 3.0;
        double r162237 = 1.0;
        double r162238 = 5.0;
        double r162239 = sqrt(r162238);
        double r162240 = r162239 - r162237;
        double r162241 = r162240 / r162218;
        double r162242 = r162241 * r162231;
        double r162243 = r162237 + r162242;
        double r162244 = r162236 - r162239;
        double r162245 = r162244 / r162218;
        double r162246 = r162245 * r162232;
        double r162247 = r162243 + r162246;
        double r162248 = r162236 * r162247;
        double r162249 = r162235 / r162248;
        return r162249;
}
↓
double f(double x, double y) {
        double r162250 = 2.0;
        double r162251 = x;
        double r162252 = sin(r162251);
        double r162253 = y;
        double r162254 = sin(r162253);
        double r162255 = 16.0;
        double r162256 = r162254 / r162255;
        double r162257 = r162252 - r162256;
        double r162258 = sqrt(r162250);
        double r162259 = r162257 * r162258;
        double r162260 = r162252 / r162255;
        double r162261 = r162254 - r162260;
        double r162262 = cos(r162251);
        double r162263 = cos(r162253);
        double r162264 = r162262 - r162263;
        double r162265 = cbrt(r162264);
        double r162266 = r162265 * r162265;
        double r162267 = r162265 * r162266;
        double r162268 = r162261 * r162267;
        double r162269 = r162259 * r162268;
        double r162270 = r162250 + r162269;
        double r162271 = 3.0;
        double r162272 = 3.0;
        double r162273 = pow(r162271, r162272);
        double r162274 = 5.0;
        double r162275 = sqrt(r162274);
        double r162276 = r162275 * r162274;
        double r162277 = r162273 - r162276;
        double r162278 = r162271 + r162275;
        double r162279 = r162271 * r162278;
        double r162280 = r162279 + r162274;
        double r162281 = r162277 / r162280;
        double r162282 = r162281 / r162250;
        double r162283 = r162282 * r162263;
        double r162284 = 1.0;
        double r162285 = r162275 - r162284;
        double r162286 = r162285 / r162250;
        double r162287 = r162262 * r162286;
        double r162288 = r162287 + r162284;
        double r162289 = r162283 + r162288;
        double r162290 = r162271 * r162289;
        double r162291 = r162270 / r162290;
        return r162291;
}

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. Simplified0.5

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

  4. Applied add-cube-cbrt0.5

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

  6. Applied flip3--0.5

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

  7. Simplified0.5

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

  8. Simplified0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2019194 
(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))))))