Average Error: 0.5 → 0.5
Time: 36.6s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \sqrt[3]{\cos x - \cos y}\right)\right)\right)}{\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + 1\right)\right) \cdot 3}\]
\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)}{\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + 1\right)\right) \cdot 3}
double f(double x, double y) {
        double r183160 = 2.0;
        double r183161 = sqrt(r183160);
        double r183162 = x;
        double r183163 = sin(r183162);
        double r183164 = y;
        double r183165 = sin(r183164);
        double r183166 = 16.0;
        double r183167 = r183165 / r183166;
        double r183168 = r183163 - r183167;
        double r183169 = r183161 * r183168;
        double r183170 = r183163 / r183166;
        double r183171 = r183165 - r183170;
        double r183172 = r183169 * r183171;
        double r183173 = cos(r183162);
        double r183174 = cos(r183164);
        double r183175 = r183173 - r183174;
        double r183176 = r183172 * r183175;
        double r183177 = r183160 + r183176;
        double r183178 = 3.0;
        double r183179 = 1.0;
        double r183180 = 5.0;
        double r183181 = sqrt(r183180);
        double r183182 = r183181 - r183179;
        double r183183 = r183182 / r183160;
        double r183184 = r183183 * r183173;
        double r183185 = r183179 + r183184;
        double r183186 = r183178 - r183181;
        double r183187 = r183186 / r183160;
        double r183188 = r183187 * r183174;
        double r183189 = r183185 + r183188;
        double r183190 = r183178 * r183189;
        double r183191 = r183177 / r183190;
        return r183191;
}
↓
double f(double x, double y) {
        double r183192 = 2.0;
        double r183193 = x;
        double r183194 = sin(r183193);
        double r183195 = y;
        double r183196 = sin(r183195);
        double r183197 = 16.0;
        double r183198 = r183196 / r183197;
        double r183199 = r183194 - r183198;
        double r183200 = sqrt(r183192);
        double r183201 = r183199 * r183200;
        double r183202 = r183194 / r183197;
        double r183203 = r183196 - r183202;
        double r183204 = cos(r183193);
        double r183205 = cos(r183195);
        double r183206 = r183204 - r183205;
        double r183207 = cbrt(r183206);
        double r183208 = r183207 * r183207;
        double r183209 = r183207 * r183208;
        double r183210 = r183203 * r183209;
        double r183211 = r183201 * r183210;
        double r183212 = r183192 + r183211;
        double r183213 = 3.0;
        double r183214 = r183213 * r183213;
        double r183215 = 5.0;
        double r183216 = r183214 - r183215;
        double r183217 = sqrt(r183215);
        double r183218 = r183213 + r183217;
        double r183219 = r183216 / r183218;
        double r183220 = r183219 / r183192;
        double r183221 = r183220 * r183205;
        double r183222 = 1.0;
        double r183223 = r183217 - r183222;
        double r183224 = r183223 / r183192;
        double r183225 = r183204 * r183224;
        double r183226 = r183225 + r183222;
        double r183227 = r183221 + r183226;
        double r183228 = r183227 * r183213;
        double r183229 = r183212 / r183228;
        return r183229;
}

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 flip--0.5

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

  7. Simplified0.5

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

  8. Final simplification0.5

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

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))))))