\[\cos \left(x + \varepsilon\right) - \cos x
\]
↓
\[\begin{array}{l}
\mathbf{if}\;\varepsilon \leq -0.0028:\\
\;\;\;\;\left(\cos x \cdot \cos \varepsilon - \cos x\right) + \frac{\sin \varepsilon}{\frac{\sin x}{-{\sin x}^{2}}}\\
\mathbf{elif}\;\varepsilon \leq 0.0021:\\
\;\;\;\;0.041666666666666664 \cdot \left(\cos x \cdot {\varepsilon}^{4}\right) + \left(0.16666666666666666 \cdot \left(\sin x \cdot {\varepsilon}^{3}\right) + \left(-0.5 \cdot \left(\cos x \cdot {\varepsilon}^{2}\right) - \varepsilon \cdot \sin x\right)\right)\\
\mathbf{else}:\\
\;\;\;\;\left(\mathsf{fma}\left(\cos \varepsilon, \cos x, \sin \varepsilon \cdot \left(-\sin x\right)\right) - \cos x\right) + \mathsf{fma}\left(-\sin \varepsilon, \sin x, \sin \varepsilon \cdot \sin x\right)\\
\end{array}
\]
double code(double x, double eps) {
return cos((x + eps)) - cos(x);
}
↓
double code(double x, double eps) {
double tmp;
if (eps <= -0.0028) {
tmp = ((cos(x) * cos(eps)) - cos(x)) + (sin(eps) / (sin(x) / -pow(sin(x), 2.0)));
} else if (eps <= 0.0021) {
tmp = (0.041666666666666664 * (cos(x) * pow(eps, 4.0))) + ((0.16666666666666666 * (sin(x) * pow(eps, 3.0))) + ((-0.5 * (cos(x) * pow(eps, 2.0))) - (eps * sin(x))));
} else {
tmp = (fma(cos(eps), cos(x), (sin(eps) * -sin(x))) - cos(x)) + fma(-sin(eps), sin(x), (sin(eps) * sin(x)));
}
return tmp;
}
function code(x, eps)
return Float64(cos(Float64(x + eps)) - cos(x))
end
↓
function code(x, eps)
tmp = 0.0
if (eps <= -0.0028)
tmp = Float64(Float64(Float64(cos(x) * cos(eps)) - cos(x)) + Float64(sin(eps) / Float64(sin(x) / Float64(-(sin(x) ^ 2.0)))));
elseif (eps <= 0.0021)
tmp = Float64(Float64(0.041666666666666664 * Float64(cos(x) * (eps ^ 4.0))) + Float64(Float64(0.16666666666666666 * Float64(sin(x) * (eps ^ 3.0))) + Float64(Float64(-0.5 * Float64(cos(x) * (eps ^ 2.0))) - Float64(eps * sin(x)))));
else
tmp = Float64(Float64(fma(cos(eps), cos(x), Float64(sin(eps) * Float64(-sin(x)))) - cos(x)) + fma(Float64(-sin(eps)), sin(x), Float64(sin(eps) * sin(x))));
end
return tmp
end
code[x_, eps_] := N[(N[Cos[N[(x + eps), $MachinePrecision]], $MachinePrecision] - N[Cos[x], $MachinePrecision]), $MachinePrecision]
↓
code[x_, eps_] := If[LessEqual[eps, -0.0028], N[(N[(N[(N[Cos[x], $MachinePrecision] * N[Cos[eps], $MachinePrecision]), $MachinePrecision] - N[Cos[x], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[eps], $MachinePrecision] / N[(N[Sin[x], $MachinePrecision] / (-N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[eps, 0.0021], N[(N[(0.041666666666666664 * N[(N[Cos[x], $MachinePrecision] * N[Power[eps, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(0.16666666666666666 * N[(N[Sin[x], $MachinePrecision] * N[Power[eps, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-0.5 * N[(N[Cos[x], $MachinePrecision] * N[Power[eps, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(eps * N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Cos[eps], $MachinePrecision] * N[Cos[x], $MachinePrecision] + N[(N[Sin[eps], $MachinePrecision] * (-N[Sin[x], $MachinePrecision])), $MachinePrecision]), $MachinePrecision] - N[Cos[x], $MachinePrecision]), $MachinePrecision] + N[((-N[Sin[eps], $MachinePrecision]) * N[Sin[x], $MachinePrecision] + N[(N[Sin[eps], $MachinePrecision] * N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]
\cos \left(x + \varepsilon\right) - \cos x
↓
\begin{array}{l}
\mathbf{if}\;\varepsilon \leq -0.0028:\\
\;\;\;\;\left(\cos x \cdot \cos \varepsilon - \cos x\right) + \frac{\sin \varepsilon}{\frac{\sin x}{-{\sin x}^{2}}}\\
\mathbf{elif}\;\varepsilon \leq 0.0021:\\
\;\;\;\;0.041666666666666664 \cdot \left(\cos x \cdot {\varepsilon}^{4}\right) + \left(0.16666666666666666 \cdot \left(\sin x \cdot {\varepsilon}^{3}\right) + \left(-0.5 \cdot \left(\cos x \cdot {\varepsilon}^{2}\right) - \varepsilon \cdot \sin x\right)\right)\\
\mathbf{else}:\\
\;\;\;\;\left(\mathsf{fma}\left(\cos \varepsilon, \cos x, \sin \varepsilon \cdot \left(-\sin x\right)\right) - \cos x\right) + \mathsf{fma}\left(-\sin \varepsilon, \sin x, \sin \varepsilon \cdot \sin x\right)\\
\end{array}