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;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 27.2

$\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}$
2. Using strategy rm

$\leadsto \color{blue}{\left(\sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}} \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}\right) \cdot \sqrt[3]{\frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}}}}$
4. Using strategy rm

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

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