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int64 -30,985
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-6,736 | \frac{9}{100} + 9/10 = \dfrac{9}{100} + \frac{90}{100} |
5,579 | m*4 + 2 = (1 + 2 m)*2 |
22,620 | (-b + a) \times \left(a^{k + \left(-1\right)} + a^{k + 2 \times \left(-1\right)} \times b + a^{k + 3 \times (-1)} \times b \times b + \cdots + a \times a \times b^{3 \times \left(-1\right) + k} + b^{k + 2 \times \left(-1\right)} \times a + b^{(-1) + k}\right) = a^k - b^k |
34,988 | (2 \cdot 2 + 1^2)^{1 / 2} = 5^{\dfrac{1}{2}} |
10,260 | \tan^{-1}\left(1\right) = \frac14\pi |
26,689 | 1 + \lambda * \lambda - \lambda*2 = (\lambda + (-1)) * (\lambda + (-1)) |
-1,452 | -\frac{1}{4}*\dfrac{1}{8}3 = \left((-1)*1/4\right)/(8*1/3) |
16,034 | 1111 = 1 + x + x^2 + x x^2 = x^{12} |
-22,941 | 63/54 = \frac{9 \cdot 7}{6 \cdot 9} |
34,896 | 24 = \left(-1\right) + \dfrac{100}{4} |
18,933 | \sin(3\cdot x) = \sin\left(2\cdot x + x\right) = \sin(2\cdot x)\cdot \cos(x) + \cos(2\cdot x)\cdot \sin(x) |
35,035 | |16 - x*2| = 5\Longrightarrow x = 5.5, 10.5 |
-509 | -\pi*26 + \pi*\frac{323}{12} = \pi*11/12 |
-4,122 | \dfrac78 \cdot \frac{m^3}{m^3} = \frac{7 \cdot m^3}{8 \cdot m^3} |
29,354 | c \gt -1 \Rightarrow c + 1 > 0 |
-18,347 | \frac{1}{32 + k^2 + k \cdot 12} \cdot \left(k^2 + 4 \cdot k\right) = \frac{(k + 4) \cdot k}{(4 + k) \cdot (8 + k)} |
16,079 | (x + t)^1 = x + t = x^1 + t^1 |
-5,323 | 2.4\cdot 10^{3 - -2} = 10^5\cdot 2.4 |
8,704 | \cos(x - y) = \sin{y}\cdot \sin{x} + \cos{y}\cdot \cos{x} |
21,776 | w' \cdot I + I \cdot w = I \cdot (w + w') |
10,159 | \frac{1}{5}*(5*y + 1) = 1/5 + y |
3,212 | x \cdot \Sigma \cdot x^R = x \cdot \Sigma \cdot x^R \cdot x \cdot \Sigma \cdot x^R = x \cdot \Sigma^2 \cdot x^R |
7,718 | \frac{x}{y} \cdot x \cdot y = \dfrac{x}{y} \cdot y \cdot x |
50,003 | 15 = 5 + 0 + 1 + 2 + 3 + 4 |
24,051 | M'_{ii}=M_{ii} |
-24,496 | 1 + \frac166 = 1 + 1 = 1 + 1 = 2 |
29,249 | 2^n - 2^{2 \cdot (-1) + n} \cdot ((-1) + n) + 2^{4 \cdot (-1) + n} \cdot \left(2 \cdot \left(-1\right) + n\right) \cdot \left(n + 3 \cdot (-1)\right)/2! - ... = 1 + n |
-25,765 | \frac{d}{dp} (-\dfrac3p) = \frac{1}{p^2} \cdot 3 |
1,320 | \dfrac{\sin(z)}{z} = \dfrac1z(z - z^3/6 + \cdots) = 1 - \frac{z^2}{6} + \cdots |
39,041 | 7*12 + 13(-1) = 71 |
3,422 | e^{-\int_W^T s*r\,\mathrm{d}s} = e^{-\int_W^T s*r\,\mathrm{d}s} |
4,891 | \frac{1}{\dfrac1a\times c} = a/c |
16,407 | \frac{1}{\cos^2\left(y\right)} = 1 + \tan^2(y) |
30,361 | \frac{1}{100}84*83/99 = 6972/9900 \approx 0.704 |
11,621 | 0 = x^4 + 6*x^2 + 25 = \left(x^2 + 5\right)^2 - 4*x * x = (x^2 - 2*x + 5)*(x^2 + 2*x + 5) |
29,611 | (-2\cdot 3 + 2) + \left(2\cdot (-1) + 3\right)\cdot 3 - 1\cdot (2\cdot (-1) + 1) = 0 |
12,565 | x^{5/2} = \frac{1}{x^{\frac12}}\cdot x^3 |
-20,418 | -\frac25\cdot \frac{9}{9} = -\frac{18}{45} |
-10,414 | \frac{1}{r*10 + 10 (-1)} 60 = \dfrac{10}{10}*\frac{1}{(-1) + r} 6 |
20,971 | \frac{\mathrm{d}}{\mathrm{d}y} \cosh(y) = \sinh(y) |
40,600 | i^2 \cdot i = i^{2 + 1} = i^2\cdot i = -i = -i |
5,020 | |x| = (x \times x)^{\frac{1}{2}} \lt (x^2 + 1)^{\frac{1}{2}} |
8,351 | \left(b + a\right)/d = \frac{1}{d}b + \frac{1}{d}a |
-24,591 | 4*4 4 = 4*16 = 64 |
21,809 | \frac{\sin^2{z}}{1 + \sin^2{z}} = 1 - \frac{1}{1 + \sin^2{z}} = 1 - \tfrac{\sec^2{z}}{2 \cdot \tan^2{z} + 1} |
-2,458 | 4 \cdot \sqrt{7} - \sqrt{7} \cdot 2 = -\sqrt{7} \cdot \sqrt{4} + \sqrt{16} \cdot \sqrt{7} |
4,869 | \cos{z} = \sin(-z + \frac{π}{2}) |
-12,157 | \frac35 = \dfrac{t}{10 \cdot \pi} \cdot 10 \cdot \pi = t |
16,904 | 7^{5 + 10 \cdot 427} = \left(7^{10}\right)^{427} \cdot 7^5 |
5,713 | 1 - y^2 + 1 = -y \cdot y + 2 |
-18,948 | 3/10 = A_s/(64\cdot \pi)\cdot 64\cdot \pi = A_s |
-22,379 | 42 + x * x + 13*x = (x + 6)*(x + 7) |
16,739 | A\times A\times B = -A\times B\times A = B\times A\times A |
1,854 | |p| E_2 |x| E_1 = |p| |x| E_2 E_1 |
24,028 | \sin^2{y/2} = \frac{1}{2} \cdot \left(1 - \cos{y}\right) = (1 - \sqrt{1 - \sin^2{y}})/2 |
9,000 | \sqrt{y^2 - 5y + 4} = \sqrt{\left(y + (-1)\right) (y + 4(-1))} = \sqrt{y + (-1)} \sqrt{y + 4(-1)} |
-6,352 | \frac{3}{4\cdot r + 8\cdot \left(-1\right)} = \frac{3}{4\cdot (2\cdot \left(-1\right) + r)} |
29,073 | \lim_{x \to \infty} (1 - \frac{1}{x})^x = \lim_{x \to \infty} (\frac1x\cdot (x + (-1)))^x = \lim_{x \to \infty} (\frac{1}{x + (-1)}\cdot x)^{-x} = \lim_{x \to \infty} (1 + \frac{1}{x + (-1)})^{-x} |
10,175 | 2 \cdot \left(a \cdot a + d^2\right) = (d + a)^2 + (-d + a)^2 |
47,886 | \cos(A + G) + \cos\left(A - G\right) = 2*\cos{A}*\cos{G} = 2*\cos{\dfrac{1}{2}*(A + G + A - G)}*\cos{(A + G - A + G)/2} |
32,407 | -y + p \cdot p - y \cdot p = 0 \implies p = (y \pm \sqrt{y^2 + 4 \cdot y})/2 |
22,789 | \frac{\mathrm{d}y}{\mathrm{d}z} \cdot \left(z + y^2\right) = 1\Longrightarrow \frac{\mathrm{d}z}{\mathrm{d}y} = z + y^2 |
-4,604 | \frac{24\cdot (-1) + y\cdot 2}{y^2 - 3\cdot y + 10\cdot (-1)} = \frac{4}{y + 2} - \frac{2}{5\cdot \left(-1\right) + y} |
-1,380 | (1/7\cdot (-9))/(1/7\cdot (-9)) = -7/9\cdot (-9/7) |
-23,220 | 5/9 = 1 - \tfrac19*4 |
55,290 | 2\implies 3 |
27,116 | \left(h \cdot a + a^2 + h^2\right)/3 = ((a + h)/2) \cdot ((a + h)/2) + \left(h - a\right) \cdot \left(h - a\right)/12 |
-9,709 | -\tfrac{1}{2} = -\dfrac24 |
18,282 | \operatorname{E}(2 \operatorname{E}(r) r) = 2 \operatorname{E}(r) \operatorname{E}(r) |
3,840 | (\frac1a - x^2)/(\frac1a) = 1 - a*x * x |
23,698 | \tfrac{1}{6 \cdot 6 \cdot 6} \cdot {6 \choose 3} = 20/216 = 5/54 |
21,649 | 4*\tfrac{1}{5}/4 = \dfrac15 |
24,970 | 4^y = \left(2^2\right)^y = 2^{2y} = \left(2^y\right)^2 |
-18,964 | 3/5 = \frac{E_r}{4 \cdot \pi} \cdot 4 \cdot \pi = E_r |
-22,206 | g g - 12 g + 20 = (2 (-1) + g) (g + 10 (-1)) |
-5,463 | \frac{2}{49 \cdot (-1) + k^2} = \frac{2}{\left(k + 7\right) \cdot (k + 7 \cdot (-1))} |
-18,251 | \frac{n^2 + n + 30 \cdot (-1)}{n \cdot 6 + n \cdot n} = \dfrac{1}{n \cdot \left(n + 6\right)} \cdot \left(6 + n\right) \cdot (5 \cdot \left(-1\right) + n) |
8,816 | a + b = a/b + \frac{b}{a} \lt a + b |
18,355 | 2 \cdot 32 \cdot 4^4 + 8 \cdot 28 \cdot 4^4 = 73728 |
25,343 | -8/2 + 3\cdot 3 = 9 + \dfrac12\cdot \left((-1)\cdot 8\right) |
9,860 | \frac12 \cdot (b \cdot b - d \cdot d) = \frac{1}{2} \cdot \left(b + d\right) \cdot (b - d) |
30,007 | 5*\dfrac{1}{5}*18/2 = 9 |
7,636 | (1 + l)^2 = 1 + 3 + 5 + \ldots + 2\cdot l + 1 |
7,039 | \cos(-a + \pi/2) = \sin{a} |
-3,061 | \sqrt{7} \cdot 5 = \sqrt{7} \cdot (3 + 2) |
32,038 | 1820 = {4 \choose 1} \cdot {(-1) + 12 + 4 \choose 12} |
1,304 | d^n\times d^m = d^{m + n} |
12,113 | 3 \lt (1 + z^2 - 3*z)*z \implies 0 < z^3 - z^2*3 + z + 3*(-1) |
-3,022 | \left(2\cdot (-1) + 4\right)\cdot \sqrt{10} = \sqrt{10}\cdot 2 |
6,478 | \{F\cdot S\cdot x,Q\cdot S\cdot F\} \Rightarrow S\cdot F\cdot Q = S\cdot F\cdot x |
21,732 | \dfrac16 = 1/3 - \dfrac{1}{6} |
-7,979 | (-54 + 12 \times i + 90 \times i + 20)/34 = \left(-34 + 102 \times i\right)/34 = -1 + 3 \times i |
33,093 | \frac{1}{Y \cdot X} = \tfrac{1}{X \cdot Y} |
-18,353 | \dfrac{6 \cdot n + n^2}{30 \cdot (-1) + n^2 + n} = \frac{(n + 6) \cdot n}{(n + 5 \cdot \left(-1\right)) \cdot (n + 6)} |
11,041 | \frac{g}{b^x\cdot h} = g\cdot b^{-x}/h |
-1,080 | 1/(6\cdot (-5/9)) = (\dfrac{1}{5}\cdot (-9))/6 |
22,847 | g_2 \cdot g_1 \cdot g_2 = g_2 \cdot g_1 \cdot g_2 = g_2 \cdot g_1 \cdot g_2 |
5,946 | \sqrt{a \cdot a - 16 \cdot a + 48} = \sqrt{(a + 6 \cdot (-1))^2 + 12} \gt \sqrt{(a + 6 \cdot (-1))^2} = |a + 6 \cdot (-1)| = 6 - a |
-4,883 | 10^{5*\left(-1\right) + 11}*0.49 = 10^6*0.49 |
16,915 | \cos((-x + \pi)/2) = \sin(x/2) |
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