Average Error: 1.2 → 1.2
Time: 15.0s
Precision: 64
$\sin^{-1} \left(x + 1\right) - \sin^{-1} x$
$\frac{\sin^{-1} \left(x + 1\right) \cdot \left(\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right)\right) - \sin^{-1} x \cdot \left(\sin^{-1} x \cdot \sin^{-1} x\right)}{\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right) + \left(\sin^{-1} x \cdot \sin^{-1} x + \sin^{-1} \left(x + 1\right) \cdot \sin^{-1} x\right)}$
\sin^{-1} \left(x + 1\right) - \sin^{-1} x
\frac{\sin^{-1} \left(x + 1\right) \cdot \left(\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right)\right) - \sin^{-1} x \cdot \left(\sin^{-1} x \cdot \sin^{-1} x\right)}{\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right) + \left(\sin^{-1} x \cdot \sin^{-1} x + \sin^{-1} \left(x + 1\right) \cdot \sin^{-1} x\right)}
double f(double x) {
double r21968033 = x;
double r21968034 = 1.0;
double r21968035 = r21968033 + r21968034;
double r21968036 = asin(r21968035);
double r21968037 = asin(r21968033);
double r21968038 = r21968036 - r21968037;
return r21968038;
}


double f(double x) {
double r21968039 = x;
double r21968040 = 1.0;
double r21968041 = r21968039 + r21968040;
double r21968042 = asin(r21968041);
double r21968043 = r21968042 * r21968042;
double r21968044 = r21968042 * r21968043;
double r21968045 = asin(r21968039);
double r21968046 = r21968045 * r21968045;
double r21968047 = r21968045 * r21968046;
double r21968048 = r21968044 - r21968047;
double r21968049 = r21968042 * r21968045;
double r21968050 = r21968046 + r21968049;
double r21968051 = r21968043 + r21968050;
double r21968052 = r21968048 / r21968051;
return r21968052;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 1.2

$\sin^{-1} \left(x + 1\right) - \sin^{-1} x$
2. Using strategy rm
3. Applied flip3--1.2

$\leadsto \color{blue}{\frac{{\left(\sin^{-1} \left(x + 1\right)\right)}^{3} - {\left(\sin^{-1} x\right)}^{3}}{\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right) + \left(\sin^{-1} x \cdot \sin^{-1} x + \sin^{-1} \left(x + 1\right) \cdot \sin^{-1} x\right)}}$
4. Simplified1.2

$\leadsto \frac{\color{blue}{\left(\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right)\right) \cdot \sin^{-1} \left(x + 1\right) - \sin^{-1} x \cdot \left(\sin^{-1} x \cdot \sin^{-1} x\right)}}{\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right) + \left(\sin^{-1} x \cdot \sin^{-1} x + \sin^{-1} \left(x + 1\right) \cdot \sin^{-1} x\right)}$
5. Final simplification1.2

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

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "asin(x+1)-asin(x)"
(- (asin (+ x 1.0)) (asin x)))