\[\frac{1 - \cos x}{x \cdot x}\]

↓

\[\frac{\frac{\sin x}{x} \cdot \frac{\sin x}{x}}{e^{\log \left(1 + \cos x\right)}}\]

double f(double x) {
        double r1884235 = 1.0;
        double r1884236 = x;
        double r1884237 = cos(r1884236);
        double r1884238 = r1884235 - r1884237;
        double r1884239 = r1884236 * r1884236;
        double r1884240 = r1884238 / r1884239;
        return r1884240;
}

↓

double f(double x) {
        double r1884241 = x;
        double r1884242 = sin(r1884241);
        double r1884243 = r1884242 / r1884241;
        double r1884244 = r1884243 * r1884243;
        double r1884245 = 1.0;
        double r1884246 = cos(r1884241);
        double r1884247 = r1884245 + r1884246;
        double r1884248 = log(r1884247);
        double r1884249 = exp(r1884248);
        double r1884250 = r1884244 / r1884249;
        return r1884250;
}

\frac{1 - \cos x}{x \cdot x}

↓

\frac{\frac{\sin x}{x} \cdot \frac{\sin x}{x}}{e^{\log \left(1 + \cos x\right)}}

Derivation

Initial program 30.8
\[\frac{1 - \cos x}{x \cdot x}\]
Using strategy rm
Applied flip--30.9
\[\leadsto \frac{\color{blue}{\frac{1 \cdot 1 - \cos x \cdot \cos x}{1 + \cos x}}}{x \cdot x}\]
Applied associate-/l/30.9
\[\leadsto \color{blue}{\frac{1 \cdot 1 - \cos x \cdot \cos x}{\left(x \cdot x\right) \cdot \left(1 + \cos x\right)}}\]
Simplified15.2
\[\leadsto \frac{\color{blue}{\sin x \cdot \sin x}}{\left(x \cdot x\right) \cdot \left(1 + \cos x\right)}\]
Taylor expanded around -inf 15.2
\[\leadsto \color{blue}{\frac{{\left(\sin x\right)}^{2}}{{x}^{2} \cdot \left(\cos x + 1\right)}}\]
Simplified0.3
\[\leadsto \color{blue}{\frac{\frac{\sin x}{x} \cdot \frac{\sin x}{x}}{\cos x + 1}}\]
Using strategy rm
Applied add-exp-log0.3
\[\leadsto \frac{\frac{\sin x}{x} \cdot \frac{\sin x}{x}}{\color{blue}{e^{\log \left(\cos x + 1\right)}}}\]
Final simplification0.3
\[\leadsto \frac{\frac{\sin x}{x} \cdot \frac{\sin x}{x}}{e^{\log \left(1 + \cos x\right)}}\]

Error

Derivation

Reproduce