Average Error: 27.2 → 27.3
Time: 14.1s
Precision: 64
\[\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}\]
\[\left(\sqrt[3]{\frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}} \cdot \frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}}}\right) \cdot \left(\sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}} \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}\right)\]
\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}
\left(\sqrt[3]{\frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}} \cdot \frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}}}\right) \cdot \left(\sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}} \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}\right)
double f(double x) {
        double r53939251 = x;
        double r53939252 = sqrt(r53939251);
        double r53939253 = sin(r53939252);
        double r53939254 = r53939253 / r53939252;
        return r53939254;
}

double f(double x) {
        double r53939255 = x;
        double r53939256 = sqrt(r53939255);
        double r53939257 = sin(r53939256);
        double r53939258 = cbrt(r53939257);
        double r53939259 = cbrt(r53939256);
        double r53939260 = r53939258 / r53939259;
        double r53939261 = r53939260 * r53939260;
        double r53939262 = cbrt(r53939261);
        double r53939263 = cbrt(r53939260);
        double r53939264 = r53939262 * r53939263;
        double r53939265 = r53939257 / r53939256;
        double r53939266 = cbrt(r53939265);
        double r53939267 = r53939266 * r53939266;
        double r53939268 = r53939264 * r53939267;
        return r53939268;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 27.2

    \[\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}\]
  2. Using strategy rm
  3. Applied add-cube-cbrt27.3

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}} \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}\right) \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}}\]
  4. Using strategy rm
  5. Applied add-cube-cbrt27.4

    \[\leadsto \left(\sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}} \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}\right) \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\color{blue}{\left(\sqrt[3]{\sqrt{x}} \cdot \sqrt[3]{\sqrt{x}}\right) \cdot \sqrt[3]{\sqrt{x}}}}}\]
  6. Applied add-cube-cbrt27.3

    \[\leadsto \left(\sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}} \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}\right) \cdot \sqrt[3]{\frac{\color{blue}{\left(\sqrt[3]{\sin \left(\sqrt{x}\right)} \cdot \sqrt[3]{\sin \left(\sqrt{x}\right)}\right) \cdot \sqrt[3]{\sin \left(\sqrt{x}\right)}}}{\left(\sqrt[3]{\sqrt{x}} \cdot \sqrt[3]{\sqrt{x}}\right) \cdot \sqrt[3]{\sqrt{x}}}}\]
  7. Applied times-frac27.3

    \[\leadsto \left(\sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}} \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}\right) \cdot \sqrt[3]{\color{blue}{\frac{\sqrt[3]{\sin \left(\sqrt{x}\right)} \cdot \sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}} \cdot \sqrt[3]{\sqrt{x}}} \cdot \frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}}}}\]
  8. Applied cbrt-prod27.3

    \[\leadsto \left(\sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}} \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}\right) \cdot \color{blue}{\left(\sqrt[3]{\frac{\sqrt[3]{\sin \left(\sqrt{x}\right)} \cdot \sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}} \cdot \sqrt[3]{\sqrt{x}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}}}\right)}\]
  9. Simplified27.3

    \[\leadsto \left(\sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}} \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}\right) \cdot \left(\color{blue}{\sqrt[3]{\frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}} \cdot \frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}}}\right)\]
  10. Final simplification27.3

    \[\leadsto \left(\sqrt[3]{\frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}} \cdot \frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\sin \left(\sqrt{x}\right)}}{\sqrt[3]{\sqrt{x}}}}\right) \cdot \left(\sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}} \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sin(sqrt(x)) / sqrt(x)"
  (/ (sin (sqrt x)) (sqrt x)))