Average Error: 0.5 → 0.5
Time: 58.2s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\cos x - \cos y\right) \cdot \left(\log \left(e^{\sqrt[3]{\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}} \cdot \left(\sqrt[3]{\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}} \cdot \sqrt[3]{\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}}\right)}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(\frac{\frac{3 \cdot 3 - 5}{\sqrt{5} + 3}}{2} \cdot \cos y + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + 1\right)\right)}\]
\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 + \left(\cos x - \cos y\right) \cdot \left(\log \left(e^{\sqrt[3]{\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}} \cdot \left(\sqrt[3]{\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}} \cdot \sqrt[3]{\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}}\right)}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(\frac{\frac{3 \cdot 3 - 5}{\sqrt{5} + 3}}{2} \cdot \cos y + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + 1\right)\right)}
double f(double x, double y) {
        double r10224059 = 2.0;
        double r10224060 = sqrt(r10224059);
        double r10224061 = x;
        double r10224062 = sin(r10224061);
        double r10224063 = y;
        double r10224064 = sin(r10224063);
        double r10224065 = 16.0;
        double r10224066 = r10224064 / r10224065;
        double r10224067 = r10224062 - r10224066;
        double r10224068 = r10224060 * r10224067;
        double r10224069 = r10224062 / r10224065;
        double r10224070 = r10224064 - r10224069;
        double r10224071 = r10224068 * r10224070;
        double r10224072 = cos(r10224061);
        double r10224073 = cos(r10224063);
        double r10224074 = r10224072 - r10224073;
        double r10224075 = r10224071 * r10224074;
        double r10224076 = r10224059 + r10224075;
        double r10224077 = 3.0;
        double r10224078 = 1.0;
        double r10224079 = 5.0;
        double r10224080 = sqrt(r10224079);
        double r10224081 = r10224080 - r10224078;
        double r10224082 = r10224081 / r10224059;
        double r10224083 = r10224082 * r10224072;
        double r10224084 = r10224078 + r10224083;
        double r10224085 = r10224077 - r10224080;
        double r10224086 = r10224085 / r10224059;
        double r10224087 = r10224086 * r10224073;
        double r10224088 = r10224084 + r10224087;
        double r10224089 = r10224077 * r10224088;
        double r10224090 = r10224076 / r10224089;
        return r10224090;
}
↓
double f(double x, double y) {
        double r10224091 = 2.0;
        double r10224092 = x;
        double r10224093 = cos(r10224092);
        double r10224094 = y;
        double r10224095 = cos(r10224094);
        double r10224096 = r10224093 - r10224095;
        double r10224097 = sin(r10224092);
        double r10224098 = sin(r10224094);
        double r10224099 = 16.0;
        double r10224100 = r10224098 / r10224099;
        double r10224101 = r10224097 - r10224100;
        double r10224102 = sqrt(r10224091);
        double r10224103 = r10224101 * r10224102;
        double r10224104 = cbrt(r10224103);
        double r10224105 = r10224104 * r10224104;
        double r10224106 = r10224104 * r10224105;
        double r10224107 = exp(r10224106);
        double r10224108 = log(r10224107);
        double r10224109 = r10224097 / r10224099;
        double r10224110 = r10224098 - r10224109;
        double r10224111 = r10224108 * r10224110;
        double r10224112 = r10224096 * r10224111;
        double r10224113 = r10224091 + r10224112;
        double r10224114 = 3.0;
        double r10224115 = r10224114 * r10224114;
        double r10224116 = 5.0;
        double r10224117 = r10224115 - r10224116;
        double r10224118 = sqrt(r10224116);
        double r10224119 = r10224118 + r10224114;
        double r10224120 = r10224117 / r10224119;
        double r10224121 = r10224120 / r10224091;
        double r10224122 = r10224121 * r10224095;
        double r10224123 = 1.0;
        double r10224124 = r10224118 - r10224123;
        double r10224125 = r10224124 / r10224091;
        double r10224126 = r10224093 * r10224125;
        double r10224127 = r10224126 + r10224123;
        double r10224128 = r10224122 + r10224127;
        double r10224129 = r10224114 * r10224128;
        double r10224130 = r10224113 / r10224129;
        return r10224130;
}

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

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

  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-log-exp0.5

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

  8. Applied add-cube-cbrt0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2019168 
(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))))))