Average Error: 0.5 → 0.5
Time: 18.2s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{\frac{2 + \left(\left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \cos x + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(-\cos y\right)\right)}{3}}{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y}\]
\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{\frac{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 \cos x + \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 y\right)\right)}{3}}{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y}
double f(double x, double y) {
        double r234143 = 2.0;
        double r234144 = sqrt(r234143);
        double r234145 = x;
        double r234146 = sin(r234145);
        double r234147 = y;
        double r234148 = sin(r234147);
        double r234149 = 16.0;
        double r234150 = r234148 / r234149;
        double r234151 = r234146 - r234150;
        double r234152 = r234144 * r234151;
        double r234153 = r234146 / r234149;
        double r234154 = r234148 - r234153;
        double r234155 = r234152 * r234154;
        double r234156 = cos(r234145);
        double r234157 = cos(r234147);
        double r234158 = r234156 - r234157;
        double r234159 = r234155 * r234158;
        double r234160 = r234143 + r234159;
        double r234161 = 3.0;
        double r234162 = 1.0;
        double r234163 = 5.0;
        double r234164 = sqrt(r234163);
        double r234165 = r234164 - r234162;
        double r234166 = r234165 / r234143;
        double r234167 = r234166 * r234156;
        double r234168 = r234162 + r234167;
        double r234169 = r234161 - r234164;
        double r234170 = r234169 / r234143;
        double r234171 = r234170 * r234157;
        double r234172 = r234168 + r234171;
        double r234173 = r234161 * r234172;
        double r234174 = r234160 / r234173;
        return r234174;
}
↓
double f(double x, double y) {
        double r234175 = 2.0;
        double r234176 = sqrt(r234175);
        double r234177 = x;
        double r234178 = sin(r234177);
        double r234179 = y;
        double r234180 = sin(r234179);
        double r234181 = 16.0;
        double r234182 = r234180 / r234181;
        double r234183 = r234178 - r234182;
        double r234184 = r234176 * r234183;
        double r234185 = r234178 / r234181;
        double r234186 = r234180 - r234185;
        double r234187 = r234184 * r234186;
        double r234188 = cos(r234177);
        double r234189 = r234187 * r234188;
        double r234190 = cos(r234179);
        double r234191 = -r234190;
        double r234192 = r234187 * r234191;
        double r234193 = r234189 + r234192;
        double r234194 = r234175 + r234193;
        double r234195 = 3.0;
        double r234196 = r234194 / r234195;
        double r234197 = 1.0;
        double r234198 = 5.0;
        double r234199 = sqrt(r234198);
        double r234200 = r234199 - r234197;
        double r234201 = r234200 / r234175;
        double r234202 = r234201 * r234188;
        double r234203 = r234197 + r234202;
        double r234204 = r234195 - r234199;
        double r234205 = r234204 / r234175;
        double r234206 = r234205 * r234190;
        double r234207 = r234203 + r234206;
        double r234208 = r234196 / r234207;
        return r234208;
}

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 associate-/r*0.5

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

  5. Applied sub-neg0.5

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

  6. Applied distribute-lft-in0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(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))))))