Average Error: 0.5 → 0.5
Time: 11.0s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{1}{\sqrt{2}} \cdot \left(\frac{\sqrt{5} - 1}{\sqrt{2}} \cdot \cos x\right)\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
\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 + \left(\left(\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\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{1}{\sqrt{2}} \cdot \left(\frac{\sqrt{5} - 1}{\sqrt{2}} \cdot \cos x\right)\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}
double f(double x, double y) {
        double r217138 = 2.0;
        double r217139 = sqrt(r217138);
        double r217140 = x;
        double r217141 = sin(r217140);
        double r217142 = y;
        double r217143 = sin(r217142);
        double r217144 = 16.0;
        double r217145 = r217143 / r217144;
        double r217146 = r217141 - r217145;
        double r217147 = r217139 * r217146;
        double r217148 = r217141 / r217144;
        double r217149 = r217143 - r217148;
        double r217150 = r217147 * r217149;
        double r217151 = cos(r217140);
        double r217152 = cos(r217142);
        double r217153 = r217151 - r217152;
        double r217154 = r217150 * r217153;
        double r217155 = r217138 + r217154;
        double r217156 = 3.0;
        double r217157 = 1.0;
        double r217158 = 5.0;
        double r217159 = sqrt(r217158);
        double r217160 = r217159 - r217157;
        double r217161 = r217160 / r217138;
        double r217162 = r217161 * r217151;
        double r217163 = r217157 + r217162;
        double r217164 = r217156 - r217159;
        double r217165 = r217164 / r217138;
        double r217166 = r217165 * r217152;
        double r217167 = r217163 + r217166;
        double r217168 = r217156 * r217167;
        double r217169 = r217155 / r217168;
        return r217169;
}
↓
double f(double x, double y) {
        double r217170 = 2.0;
        double r217171 = sqrt(r217170);
        double r217172 = cbrt(r217171);
        double r217173 = r217172 * r217172;
        double r217174 = x;
        double r217175 = sin(r217174);
        double r217176 = y;
        double r217177 = sin(r217176);
        double r217178 = 16.0;
        double r217179 = r217177 / r217178;
        double r217180 = r217175 - r217179;
        double r217181 = r217172 * r217180;
        double r217182 = r217173 * r217181;
        double r217183 = r217175 / r217178;
        double r217184 = r217177 - r217183;
        double r217185 = r217182 * r217184;
        double r217186 = cos(r217174);
        double r217187 = cos(r217176);
        double r217188 = r217186 - r217187;
        double r217189 = r217185 * r217188;
        double r217190 = r217170 + r217189;
        double r217191 = 3.0;
        double r217192 = 1.0;
        double r217193 = 1.0;
        double r217194 = r217193 / r217171;
        double r217195 = 5.0;
        double r217196 = sqrt(r217195);
        double r217197 = r217196 - r217192;
        double r217198 = r217197 / r217171;
        double r217199 = r217198 * r217186;
        double r217200 = r217194 * r217199;
        double r217201 = r217192 + r217200;
        double r217202 = r217191 - r217196;
        double r217203 = r217202 / r217170;
        double r217204 = r217203 * r217187;
        double r217205 = r217201 + r217204;
        double r217206 = r217191 * r217205;
        double r217207 = r217190 / r217206;
        return r217207;
}

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 add-sqr-sqrt0.5

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

  4. Applied *-un-lft-identity0.5

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

  5. Applied times-frac0.5

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

  6. Applied associate-*l*0.5

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

  8. Applied add-cube-cbrt0.5

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

  9. Applied associate-*l*0.5

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

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2020018 
(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))))))