Average Error: 26.4 → 0.5
Time: 13.2s
Precision: 64
$\frac{\sin x}{\sin \left(1 + x\right)}$
$\frac{\sin x}{\frac{{\left(\sin 1 \cdot \cos x\right)}^{3} + {\left(\sin x \cdot \cos 1\right)}^{3}}{{\left(\sin 1\right)}^{2} \cdot \left(\cos x \cdot \cos x\right) + \left(\sin x \cdot \cos 1\right) \cdot \left(\sin x \cdot \cos 1 - \sin 1 \cdot \cos x\right)}}$
\frac{\sin x}{\sin \left(1 + x\right)}
\frac{\sin x}{\frac{{\left(\sin 1 \cdot \cos x\right)}^{3} + {\left(\sin x \cdot \cos 1\right)}^{3}}{{\left(\sin 1\right)}^{2} \cdot \left(\cos x \cdot \cos x\right) + \left(\sin x \cdot \cos 1\right) \cdot \left(\sin x \cdot \cos 1 - \sin 1 \cdot \cos x\right)}}
double f(double x) {
double r1952361 = x;
double r1952362 = sin(r1952361);
double r1952363 = 1.0;
double r1952364 = r1952363 + r1952361;
double r1952365 = sin(r1952364);
double r1952366 = r1952362 / r1952365;
return r1952366;
}


double f(double x) {
double r1952367 = x;
double r1952368 = sin(r1952367);
double r1952369 = 1.0;
double r1952370 = sin(r1952369);
double r1952371 = cos(r1952367);
double r1952372 = r1952370 * r1952371;
double r1952373 = 3.0;
double r1952374 = pow(r1952372, r1952373);
double r1952375 = cos(r1952369);
double r1952376 = r1952368 * r1952375;
double r1952377 = pow(r1952376, r1952373);
double r1952378 = r1952374 + r1952377;
double r1952379 = 2.0;
double r1952380 = pow(r1952370, r1952379);
double r1952381 = r1952371 * r1952371;
double r1952382 = r1952380 * r1952381;
double r1952383 = r1952376 - r1952372;
double r1952384 = r1952376 * r1952383;
double r1952385 = r1952382 + r1952384;
double r1952386 = r1952378 / r1952385;
double r1952387 = r1952368 / r1952386;
return r1952387;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 26.4

$\frac{\sin x}{\sin \left(1 + x\right)}$
2. Using strategy rm
3. Applied sin-sum0.4

$\leadsto \frac{\sin x}{\color{blue}{\sin 1 \cdot \cos x + \cos 1 \cdot \sin x}}$
4. Simplified0.4

$\leadsto \frac{\sin x}{\sin 1 \cdot \cos x + \color{blue}{\sin x \cdot \cos 1}}$
5. Using strategy rm
6. Applied flip3-+0.5

$\leadsto \frac{\sin x}{\color{blue}{\frac{{\left(\sin 1 \cdot \cos x\right)}^{3} + {\left(\sin x \cdot \cos 1\right)}^{3}}{\left(\sin 1 \cdot \cos x\right) \cdot \left(\sin 1 \cdot \cos x\right) + \left(\left(\sin x \cdot \cos 1\right) \cdot \left(\sin x \cdot \cos 1\right) - \left(\sin 1 \cdot \cos x\right) \cdot \left(\sin x \cdot \cos 1\right)\right)}}}$
7. Simplified0.5

$\leadsto \frac{\sin x}{\frac{{\left(\sin 1 \cdot \cos x\right)}^{3} + {\left(\sin x \cdot \cos 1\right)}^{3}}{\color{blue}{{\left(\sin 1\right)}^{2} \cdot \left(\cos x \cdot \cos x\right) + \left(\sin x \cdot \cos 1\right) \cdot \left(\sin x \cdot \cos 1 - \sin 1 \cdot \cos x\right)}}}$
8. Final simplification0.5

$\leadsto \frac{\sin x}{\frac{{\left(\sin 1 \cdot \cos x\right)}^{3} + {\left(\sin x \cdot \cos 1\right)}^{3}}{{\left(\sin 1\right)}^{2} \cdot \left(\cos x \cdot \cos x\right) + \left(\sin x \cdot \cos 1\right) \cdot \left(\sin x \cdot \cos 1 - \sin 1 \cdot \cos x\right)}}$

# Reproduce

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