Average Error: 0.2 → 0.0
Time: 8.8s
Precision: 64
$\sin x \cdot \cos x$
$\frac{\sin \left(x + x\right)}{2}$
\sin x \cdot \cos x
\frac{\sin \left(x + x\right)}{2}
double f(double x) {
double r1406352 = x;
double r1406353 = sin(r1406352);
double r1406354 = cos(r1406352);
double r1406355 = r1406353 * r1406354;
return r1406355;
}


double f(double x) {
double r1406356 = x;
double r1406357 = r1406356 + r1406356;
double r1406358 = sin(r1406357);
double r1406359 = 2.0;
double r1406360 = r1406358 / r1406359;
return r1406360;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.2

$\sin x \cdot \cos x$
2. Using strategy rm
3. Applied sin-cos-mult0.0

$\leadsto \color{blue}{\frac{\sin \left(x - x\right) + \sin \left(x + x\right)}{2}}$
4. Simplified0.0

$\leadsto \frac{\color{blue}{\sin \left(x + x\right)}}{2}$
5. Final simplification0.0

$\leadsto \frac{\sin \left(x + x\right)}{2}$

# Reproduce

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