Average Error: 0.3 → 0.3
Time: 17.5s
Precision: 64
$\sin x \cdot \left(\cos x \cdot \sin x\right)$
${\left(\sin x\right)}^{2} \cdot \cos x$
\sin x \cdot \left(\cos x \cdot \sin x\right)
{\left(\sin x\right)}^{2} \cdot \cos x
double f(double x) {
double r949145 = x;
double r949146 = sin(r949145);
double r949147 = cos(r949145);
double r949148 = r949147 * r949146;
double r949149 = r949146 * r949148;
return r949149;
}


double f(double x) {
double r949150 = x;
double r949151 = sin(r949150);
double r949152 = 2.0;
double r949153 = pow(r949151, r949152);
double r949154 = cos(r949150);
double r949155 = r949153 * r949154;
return r949155;
}



Try it out

Results

 In Out
Enter valid numbers for all inputs

Derivation

1. Initial program 0.3

$\sin x \cdot \left(\cos x \cdot \sin x\right)$
2. Taylor expanded around inf 0.3

$\leadsto \color{blue}{{\left(\sin x\right)}^{2} \cdot \cos x}$
3. Final simplification0.3

$\leadsto {\left(\sin x\right)}^{2} \cdot \cos x$

Reproduce

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