Average Error: 27.4 → 27.3
Time: 14.0s
Precision: 64
\[\sin \left(\sqrt{x} + 1\right) + \cos \left(\sqrt{x}\right)\]
\[\left(\sqrt[3]{{\left(\cos 1 \cdot \sin \left(\sqrt{x}\right)\right)}^{3}} + \cos \left(\sqrt{x}\right) \cdot \sin 1\right) + \cos \left(\sqrt{x}\right)\]
\sin \left(\sqrt{x} + 1\right) + \cos \left(\sqrt{x}\right)
\left(\sqrt[3]{{\left(\cos 1 \cdot \sin \left(\sqrt{x}\right)\right)}^{3}} + \cos \left(\sqrt{x}\right) \cdot \sin 1\right) + \cos \left(\sqrt{x}\right)
double f(double x) {
        double r861132 = x;
        double r861133 = sqrt(r861132);
        double r861134 = 1.0;
        double r861135 = r861133 + r861134;
        double r861136 = sin(r861135);
        double r861137 = cos(r861133);
        double r861138 = r861136 + r861137;
        return r861138;
}

double f(double x) {
        double r861139 = 1.0;
        double r861140 = cos(r861139);
        double r861141 = x;
        double r861142 = sqrt(r861141);
        double r861143 = sin(r861142);
        double r861144 = r861140 * r861143;
        double r861145 = 3.0;
        double r861146 = pow(r861144, r861145);
        double r861147 = cbrt(r861146);
        double r861148 = cos(r861142);
        double r861149 = sin(r861139);
        double r861150 = r861148 * r861149;
        double r861151 = r861147 + r861150;
        double r861152 = r861151 + r861148;
        return r861152;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 27.4

    \[\sin \left(\sqrt{x} + 1\right) + \cos \left(\sqrt{x}\right)\]
  2. Using strategy rm
  3. Applied sin-sum27.3

    \[\leadsto \color{blue}{\left(\sin \left(\sqrt{x}\right) \cdot \cos 1 + \cos \left(\sqrt{x}\right) \cdot \sin 1\right)} + \cos \left(\sqrt{x}\right)\]
  4. Using strategy rm
  5. Applied add-cbrt-cube27.3

    \[\leadsto \left(\sin \left(\sqrt{x}\right) \cdot \color{blue}{\sqrt[3]{\left(\cos 1 \cdot \cos 1\right) \cdot \cos 1}} + \cos \left(\sqrt{x}\right) \cdot \sin 1\right) + \cos \left(\sqrt{x}\right)\]
  6. Applied add-cbrt-cube27.3

    \[\leadsto \left(\color{blue}{\sqrt[3]{\left(\sin \left(\sqrt{x}\right) \cdot \sin \left(\sqrt{x}\right)\right) \cdot \sin \left(\sqrt{x}\right)}} \cdot \sqrt[3]{\left(\cos 1 \cdot \cos 1\right) \cdot \cos 1} + \cos \left(\sqrt{x}\right) \cdot \sin 1\right) + \cos \left(\sqrt{x}\right)\]
  7. Applied cbrt-unprod27.3

    \[\leadsto \left(\color{blue}{\sqrt[3]{\left(\left(\sin \left(\sqrt{x}\right) \cdot \sin \left(\sqrt{x}\right)\right) \cdot \sin \left(\sqrt{x}\right)\right) \cdot \left(\left(\cos 1 \cdot \cos 1\right) \cdot \cos 1\right)}} + \cos \left(\sqrt{x}\right) \cdot \sin 1\right) + \cos \left(\sqrt{x}\right)\]
  8. Simplified27.3

    \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\cos 1 \cdot \sin \left(\sqrt{x}\right)\right)}^{3}}} + \cos \left(\sqrt{x}\right) \cdot \sin 1\right) + \cos \left(\sqrt{x}\right)\]
  9. Final simplification27.3

    \[\leadsto \left(\sqrt[3]{{\left(\cos 1 \cdot \sin \left(\sqrt{x}\right)\right)}^{3}} + \cos \left(\sqrt{x}\right) \cdot \sin 1\right) + \cos \left(\sqrt{x}\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sin(sqrt(x) + 1) + cos(sqrt(x))"
  :precision binary64
  (+ (sin (+ (sqrt x) 1)) (cos (sqrt x))))