Average Error: 58.0 → 0.3
Time: 20.8s
Precision: 64
$\sinh \left(x + 1\right) - \sinh 1$
$2 \cdot \left(\sinh \left(\frac{x}{2}\right) \cdot \left(\left(e^{x \cdot \frac{-1}{2} - 1} + \sqrt{e^{2 + x}}\right) \cdot \frac{1}{2}\right)\right)$
\sinh \left(x + 1\right) - \sinh 1
2 \cdot \left(\sinh \left(\frac{x}{2}\right) \cdot \left(\left(e^{x \cdot \frac{-1}{2} - 1} + \sqrt{e^{2 + x}}\right) \cdot \frac{1}{2}\right)\right)
double f(double x) {
double r9791279 = x;
double r9791280 = 1.0;
double r9791281 = r9791279 + r9791280;
double r9791282 = sinh(r9791281);
double r9791283 = sinh(r9791280);
double r9791284 = r9791282 - r9791283;
return r9791284;
}


double f(double x) {
double r9791285 = 2.0;
double r9791286 = x;
double r9791287 = r9791286 / r9791285;
double r9791288 = sinh(r9791287);
double r9791289 = -0.5;
double r9791290 = r9791286 * r9791289;
double r9791291 = 1.0;
double r9791292 = r9791290 - r9791291;
double r9791293 = exp(r9791292);
double r9791294 = 2.0;
double r9791295 = r9791294 + r9791286;
double r9791296 = exp(r9791295);
double r9791297 = sqrt(r9791296);
double r9791298 = r9791293 + r9791297;
double r9791299 = 0.5;
double r9791300 = r9791298 * r9791299;
double r9791301 = r9791288 * r9791300;
double r9791302 = r9791285 * r9791301;
return r9791302;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 58.0

$\sinh \left(x + 1\right) - \sinh 1$
2. Using strategy rm
3. Applied diff-sinh58.0

$\leadsto \color{blue}{2 \cdot \left(\cosh \left(\frac{\left(x + 1\right) + 1}{2}\right) \cdot \sinh \left(\frac{\left(x + 1\right) - 1}{2}\right)\right)}$
4. Simplified0.3

$\leadsto 2 \cdot \color{blue}{\left(\cosh \left(\frac{\left(x + 1\right) + 1}{2}\right) \cdot \sinh \left(\frac{x}{2}\right)\right)}$
5. Taylor expanded around inf 0.3

$\leadsto 2 \cdot \left(\color{blue}{\left(\frac{1}{2} \cdot \left(e^{-\left(\frac{1}{2} \cdot x + 1\right)} + e^{\frac{1}{2} \cdot \left(x + 2\right)}\right)\right)} \cdot \sinh \left(\frac{x}{2}\right)\right)$
6. Simplified0.3

$\leadsto 2 \cdot \left(\color{blue}{\left(\left(\sqrt{e^{2 + x}} + e^{\frac{-1}{2} \cdot x - 1}\right) \cdot \frac{1}{2}\right)} \cdot \sinh \left(\frac{x}{2}\right)\right)$
7. Final simplification0.3

$\leadsto 2 \cdot \left(\sinh \left(\frac{x}{2}\right) \cdot \left(\left(e^{x \cdot \frac{-1}{2} - 1} + \sqrt{e^{2 + x}}\right) \cdot \frac{1}{2}\right)\right)$

# Reproduce

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