Average Error: 1.0 → 0.0
Time: 54.0s
Precision: 64
• ## could not determine a ground truth for program body (more)

1. x = 1.3100436170095023e+65
$\cosh \left(x + 1\right) - \cosh x$
$2 \cdot \left(\sinh \left(\frac{1}{2}\right) \cdot \sinh \left(\frac{x + \left(x + 1\right)}{2}\right)\right)$
\cosh \left(x + 1\right) - \cosh x
2 \cdot \left(\sinh \left(\frac{1}{2}\right) \cdot \sinh \left(\frac{x + \left(x + 1\right)}{2}\right)\right)
double f(double x) {
double r23992617 = x;
double r23992618 = 1.0;
double r23992619 = r23992617 + r23992618;
double r23992620 = cosh(r23992619);
double r23992621 = cosh(r23992617);
double r23992622 = r23992620 - r23992621;
return r23992622;
}


double f(double x) {
double r23992623 = 2.0;
double r23992624 = 1.0;
double r23992625 = r23992624 / r23992623;
double r23992626 = sinh(r23992625);
double r23992627 = x;
double r23992628 = r23992627 + r23992624;
double r23992629 = r23992627 + r23992628;
double r23992630 = r23992629 / r23992623;
double r23992631 = sinh(r23992630);
double r23992632 = r23992626 * r23992631;
double r23992633 = r23992623 * r23992632;
return r23992633;
}



# Try it out

Results

 In Out
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# Derivation

1. Initial program 1.0

$\cosh \left(x + 1\right) - \cosh x$
2. Using strategy rm
3. Applied diff-cosh0.0

$\leadsto \color{blue}{2 \cdot \left(\sinh \left(\frac{\left(x + 1\right) + x}{2}\right) \cdot \sinh \left(\frac{\left(x + 1\right) - x}{2}\right)\right)}$
4. Simplified0.0

$\leadsto 2 \cdot \color{blue}{\left(\sinh \left(\frac{x + \left(1 + x\right)}{2}\right) \cdot \sinh \left(\frac{1}{2}\right)\right)}$
5. Final simplification0.0

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

# Reproduce

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