Average Error: 0.5 → 0.5
Time: 42.8s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 \cdot 2 - \left(\left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\right) \cdot \left(\left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\right)}{\left(3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\right) \cdot \left(2 - \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\right)}\]
\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 \cdot 2 - \left(\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)\right) \cdot \left(\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)\right)}{\left(3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\right) \cdot \left(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)\right)}
double f(double x, double y) {
        double r17126205 = 2.0;
        double r17126206 = sqrt(r17126205);
        double r17126207 = x;
        double r17126208 = sin(r17126207);
        double r17126209 = y;
        double r17126210 = sin(r17126209);
        double r17126211 = 16.0;
        double r17126212 = r17126210 / r17126211;
        double r17126213 = r17126208 - r17126212;
        double r17126214 = r17126206 * r17126213;
        double r17126215 = r17126208 / r17126211;
        double r17126216 = r17126210 - r17126215;
        double r17126217 = r17126214 * r17126216;
        double r17126218 = cos(r17126207);
        double r17126219 = cos(r17126209);
        double r17126220 = r17126218 - r17126219;
        double r17126221 = r17126217 * r17126220;
        double r17126222 = r17126205 + r17126221;
        double r17126223 = 3.0;
        double r17126224 = 1.0;
        double r17126225 = 5.0;
        double r17126226 = sqrt(r17126225);
        double r17126227 = r17126226 - r17126224;
        double r17126228 = r17126227 / r17126205;
        double r17126229 = r17126228 * r17126218;
        double r17126230 = r17126224 + r17126229;
        double r17126231 = r17126223 - r17126226;
        double r17126232 = r17126231 / r17126205;
        double r17126233 = r17126232 * r17126219;
        double r17126234 = r17126230 + r17126233;
        double r17126235 = r17126223 * r17126234;
        double r17126236 = r17126222 / r17126235;
        return r17126236;
}
↓
double f(double x, double y) {
        double r17126237 = 2.0;
        double r17126238 = r17126237 * r17126237;
        double r17126239 = sqrt(r17126237);
        double r17126240 = x;
        double r17126241 = sin(r17126240);
        double r17126242 = y;
        double r17126243 = sin(r17126242);
        double r17126244 = 16.0;
        double r17126245 = r17126243 / r17126244;
        double r17126246 = r17126241 - r17126245;
        double r17126247 = r17126239 * r17126246;
        double r17126248 = r17126241 / r17126244;
        double r17126249 = r17126243 - r17126248;
        double r17126250 = r17126247 * r17126249;
        double r17126251 = cos(r17126240);
        double r17126252 = cos(r17126242);
        double r17126253 = r17126251 - r17126252;
        double r17126254 = r17126250 * r17126253;
        double r17126255 = r17126254 * r17126254;
        double r17126256 = r17126238 - r17126255;
        double r17126257 = 3.0;
        double r17126258 = 1.0;
        double r17126259 = 5.0;
        double r17126260 = sqrt(r17126259);
        double r17126261 = r17126260 - r17126258;
        double r17126262 = r17126261 / r17126237;
        double r17126263 = r17126262 * r17126251;
        double r17126264 = r17126258 + r17126263;
        double r17126265 = r17126257 - r17126260;
        double r17126266 = r17126265 / r17126237;
        double r17126267 = r17126266 * r17126252;
        double r17126268 = r17126264 + r17126267;
        double r17126269 = r17126257 * r17126268;
        double r17126270 = r17126237 - r17126254;
        double r17126271 = r17126269 * r17126270;
        double r17126272 = r17126256 / r17126271;
        return r17126272;
}

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

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

  4. Applied associate-/l/0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019174 
(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))))))