Average Error: 0.5 → 0.5
Time: 37.3s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \sqrt[3]{\sqrt{2} \cdot \left(2 \cdot \left({\left(\sin x - \frac{\sin y}{16}\right)}^{3} \cdot {\left(\sin y - \frac{\sin x}{16}\right)}^{3}\right)\right)} \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
\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 \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 + \sqrt[3]{\sqrt{2} \cdot \left(2 \cdot \left({\left(\sin x - \frac{\sin y}{16}\right)}^{3} \cdot {\left(\sin y - \frac{\sin x}{16}\right)}^{3}\right)\right)} \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}
double f(double x, double y) {
        double r189134 = 2.0;
        double r189135 = sqrt(r189134);
        double r189136 = x;
        double r189137 = sin(r189136);
        double r189138 = y;
        double r189139 = sin(r189138);
        double r189140 = 16.0;
        double r189141 = r189139 / r189140;
        double r189142 = r189137 - r189141;
        double r189143 = r189135 * r189142;
        double r189144 = r189137 / r189140;
        double r189145 = r189139 - r189144;
        double r189146 = r189143 * r189145;
        double r189147 = cos(r189136);
        double r189148 = cos(r189138);
        double r189149 = r189147 - r189148;
        double r189150 = r189146 * r189149;
        double r189151 = r189134 + r189150;
        double r189152 = 3.0;
        double r189153 = 1.0;
        double r189154 = 5.0;
        double r189155 = sqrt(r189154);
        double r189156 = r189155 - r189153;
        double r189157 = r189156 / r189134;
        double r189158 = r189157 * r189147;
        double r189159 = r189153 + r189158;
        double r189160 = r189152 - r189155;
        double r189161 = r189160 / r189134;
        double r189162 = r189161 * r189148;
        double r189163 = r189159 + r189162;
        double r189164 = r189152 * r189163;
        double r189165 = r189151 / r189164;
        return r189165;
}
↓
double f(double x, double y) {
        double r189166 = 2.0;
        double r189167 = sqrt(r189166);
        double r189168 = x;
        double r189169 = sin(r189168);
        double r189170 = y;
        double r189171 = sin(r189170);
        double r189172 = 16.0;
        double r189173 = r189171 / r189172;
        double r189174 = r189169 - r189173;
        double r189175 = 3.0;
        double r189176 = pow(r189174, r189175);
        double r189177 = r189169 / r189172;
        double r189178 = r189171 - r189177;
        double r189179 = pow(r189178, r189175);
        double r189180 = r189176 * r189179;
        double r189181 = r189166 * r189180;
        double r189182 = r189167 * r189181;
        double r189183 = cbrt(r189182);
        double r189184 = cos(r189168);
        double r189185 = cos(r189170);
        double r189186 = r189184 - r189185;
        double r189187 = r189183 * r189186;
        double r189188 = r189166 + r189187;
        double r189189 = 3.0;
        double r189190 = 1.0;
        double r189191 = 5.0;
        double r189192 = sqrt(r189191);
        double r189193 = r189192 - r189190;
        double r189194 = r189193 / r189166;
        double r189195 = r189194 * r189184;
        double r189196 = r189190 + r189195;
        double r189197 = r189189 * r189189;
        double r189198 = r189197 - r189191;
        double r189199 = r189189 + r189192;
        double r189200 = r189198 / r189199;
        double r189201 = r189200 / r189166;
        double r189202 = r189201 * r189185;
        double r189203 = r189196 + r189202;
        double r189204 = r189189 * r189203;
        double r189205 = r189188 / r189204;
        return r189205;
}

Error

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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

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

  4. Simplified0.5

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

  6. Applied add-cbrt-cube0.5

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

  7. Applied add-cbrt-cube0.5

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

  8. Applied add-cbrt-cube0.5

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

  9. Applied cbrt-unprod0.5

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

  10. Applied cbrt-unprod0.5

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

  11. Simplified0.5

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

  12. Final simplification0.5

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

Reproduce

herbie shell --seed 2019305 
(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))))))