Average Error: 0.5 → 0.5
Time: 38.8s
Precision: 64
\[\frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]
↓
\[\frac{2.0 + \left(\sqrt[3]{\cos x - \cos y} \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \sqrt[3]{\cos x - \cos y}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}\right)\right)}{\left(\left(\cos x \cdot \frac{\sqrt{5.0} - 1.0}{2.0} + 1.0\right) + \cos y \cdot \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0}\right) \cdot 3.0}\]
\frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}
↓
\frac{2.0 + \left(\sqrt[3]{\cos x - \cos y} \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \sqrt[3]{\cos x - \cos y}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}\right)\right)}{\left(\left(\cos x \cdot \frac{\sqrt{5.0} - 1.0}{2.0} + 1.0\right) + \cos y \cdot \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0}\right) \cdot 3.0}
double f(double x, double y) {
        double r13727172 = 2.0;
        double r13727173 = sqrt(r13727172);
        double r13727174 = x;
        double r13727175 = sin(r13727174);
        double r13727176 = y;
        double r13727177 = sin(r13727176);
        double r13727178 = 16.0;
        double r13727179 = r13727177 / r13727178;
        double r13727180 = r13727175 - r13727179;
        double r13727181 = r13727173 * r13727180;
        double r13727182 = r13727175 / r13727178;
        double r13727183 = r13727177 - r13727182;
        double r13727184 = r13727181 * r13727183;
        double r13727185 = cos(r13727174);
        double r13727186 = cos(r13727176);
        double r13727187 = r13727185 - r13727186;
        double r13727188 = r13727184 * r13727187;
        double r13727189 = r13727172 + r13727188;
        double r13727190 = 3.0;
        double r13727191 = 1.0;
        double r13727192 = 5.0;
        double r13727193 = sqrt(r13727192);
        double r13727194 = r13727193 - r13727191;
        double r13727195 = r13727194 / r13727172;
        double r13727196 = r13727195 * r13727185;
        double r13727197 = r13727191 + r13727196;
        double r13727198 = r13727190 - r13727193;
        double r13727199 = r13727198 / r13727172;
        double r13727200 = r13727199 * r13727186;
        double r13727201 = r13727197 + r13727200;
        double r13727202 = r13727190 * r13727201;
        double r13727203 = r13727189 / r13727202;
        return r13727203;
}
↓
double f(double x, double y) {
        double r13727204 = 2.0;
        double r13727205 = x;
        double r13727206 = cos(r13727205);
        double r13727207 = y;
        double r13727208 = cos(r13727207);
        double r13727209 = r13727206 - r13727208;
        double r13727210 = cbrt(r13727209);
        double r13727211 = r13727210 * r13727210;
        double r13727212 = r13727210 * r13727211;
        double r13727213 = sin(r13727207);
        double r13727214 = sin(r13727205);
        double r13727215 = 16.0;
        double r13727216 = r13727214 / r13727215;
        double r13727217 = r13727213 - r13727216;
        double r13727218 = r13727213 / r13727215;
        double r13727219 = r13727214 - r13727218;
        double r13727220 = sqrt(r13727204);
        double r13727221 = r13727219 * r13727220;
        double r13727222 = r13727217 * r13727221;
        double r13727223 = r13727212 * r13727222;
        double r13727224 = r13727204 + r13727223;
        double r13727225 = 5.0;
        double r13727226 = sqrt(r13727225);
        double r13727227 = 1.0;
        double r13727228 = r13727226 - r13727227;
        double r13727229 = r13727228 / r13727204;
        double r13727230 = r13727206 * r13727229;
        double r13727231 = r13727230 + r13727227;
        double r13727232 = 3.0;
        double r13727233 = r13727232 * r13727232;
        double r13727234 = r13727233 - r13727225;
        double r13727235 = r13727232 + r13727226;
        double r13727236 = r13727234 / r13727235;
        double r13727237 = r13727236 / r13727204;
        double r13727238 = r13727208 * r13727237;
        double r13727239 = r13727231 + r13727238;
        double r13727240 = r13727239 * r13727232;
        double r13727241 = r13727224 / r13727240;
        return r13727241;
}

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

    \[\frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.5

    \[\leadsto \frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\cos x - \cos y} \cdot \sqrt[3]{\cos x - \cos y}\right) \cdot \sqrt[3]{\cos x - \cos y}\right)}}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]
  4. Using strategy rm

  5. Applied flip--0.5

    \[\leadsto \frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\left(\sqrt[3]{\cos x - \cos y} \cdot \sqrt[3]{\cos x - \cos y}\right) \cdot \sqrt[3]{\cos x - \cos y}\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\color{blue}{\frac{3.0 \cdot 3.0 - \sqrt{5.0} \cdot \sqrt{5.0}}{3.0 + \sqrt{5.0}}}}{2.0} \cdot \cos y\right)}\]

  6. Simplified0.5

    \[\leadsto \frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\left(\sqrt[3]{\cos x - \cos y} \cdot \sqrt[3]{\cos x - \cos y}\right) \cdot \sqrt[3]{\cos x - \cos y}\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{\color{blue}{3.0 \cdot 3.0 - 5.0}}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  7. Final simplification0.5

    \[\leadsto \frac{2.0 + \left(\sqrt[3]{\cos x - \cos y} \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \sqrt[3]{\cos x - \cos y}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \sqrt{2.0}\right)\right)}{\left(\left(\cos x \cdot \frac{\sqrt{5.0} - 1.0}{2.0} + 1.0\right) + \cos y \cdot \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0}\right) \cdot 3.0}\]

Reproduce

herbie shell --seed 2019163 
(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))))))