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int64 -30,985
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-11,175 | (z + 8(-1))^2 + f = (z + 8(-1)) (z + 8(-1)) + f = z^2 - 16 z + 64 + f |
23,136 | \left|{A + G}\right| = 0 \lt \left|{A}\right| + \left|{G}\right| |
24,497 | \cos(\operatorname{atan}(x)) = \dfrac{1}{(1 + x^2)^{1/2}} |
26,671 | 5/(9*8) + 1/(6*3) = \frac18 |
7,902 | -z^3 + x^2 \cdot x = (x \cdot x + x \cdot z + z^2) \cdot \left(-z + x\right) |
51,248 | 3 + 1 + 2 = 3 + 2 + 1 |
33,256 | 72*\left(-1\right) + 145 = 73 |
21,399 | \dfrac{4}{p + 2*(-1)} + 1 = \frac{1}{p + 2*\left(-1\right)}*(2 + p) |
23,709 | -\left(-6\right) + 2*\left(-2\right) = 2 |
-29,355 | \left(2 + 7x\right) (2 - 7x) = 2^2 - (7x)^2 = 4 - 49 x^2 |
12,852 | d \cdot d + x^2 + d\cdot x\cdot 2 = (x + d) \cdot (x + d) |
4,856 | -x^2 + 1 = \left(1 - x\right)*(1 + x) |
33,233 | 2000 = \frac12 \cdot 800 + \frac{3200}{2} |
27,414 | \ln(z + 1) = z - \dfrac12*z^2 + z^2 * z/3 - \frac14*z^4 + \dots |
17,251 | h = (w/h + h/w) \cdot x = \frac{1}{w \cdot h} \cdot (w^2 + h^2) \cdot x |
15,378 | (-\cos(\alpha + \beta) + \cos(\alpha - \beta))/2 = \sin\left(\beta\right) \cdot \sin(\alpha) |
15,655 | \tfrac{1}{C_x\cdot C}\cdot (C - C_x) = 1/\left(C_x\right) - 1/C |
2,647 | x^{N + 1} = x \cdot x^N |
14,003 | 1 > |x/2| \implies |x| < 2 |
18,142 | \cos^2(x) = \frac12\cdot (1 + \cos\left(x\cdot 2\right)) |
1,326 | (n + 1)! = (n + 1) \cdot n! \lt (n + 1) \cdot n^n = n^{n + 1} + n^n \lt n^{n + 1} + n^{n + 1} = 2 \cdot n^{n + 1} < (n + 1)^{n + 1} |
-19,673 | 18/9 = \dfrac{2*9}{9} |
19,046 | \frac{3}{3 + 2}*\frac{3}{3 + 2} = \frac{1}{25}*9 = 0.36 |
10,353 | 1 + x^2 \leq x^2*2 \Rightarrow \frac{1}{1 + x^2} \geq \frac{1}{2x^2} |
21,498 | 33 \cdot 3^m = -3 \cdot 3^m + 3^m \cdot 9 + 3^m \cdot 27 |
-20,731 | 10/7*\frac{1}{5*(-1) + r}*\left(5*(-1) + r\right) = \frac{10*r + 50*(-1)}{7*r + 35*(-1)} |
-6,017 | \tfrac{1}{5 \cdot q + 15} \cdot 4 = \frac{4}{(3 + q) \cdot 5} |
757 | \left(\sqrt{j}\right)^2 = j = 0 + j = (c + x \cdot j) \cdot (c + x \cdot j) = c^2 + 2 \cdot c \cdot x \cdot j + x^2 \cdot j^2 = c^2 - x \cdot x + 2 \cdot c \cdot x \cdot j |
13,291 | \sum_{m=1}^l \left(1 + m\right) (m + (-1)) = \sum_{m=1}^l ((-1) + m) (1 + m) |
15,845 | c*d = \frac{1}{c*d} = 1/(d*c) = d*c |
4,567 | (2^{20} + (-1)) \cdot 3 = -3 + 2^{20} \cdot 3 |
13,655 | 7 = y + (-y^2 + 9\cdot y + 1)/7 = (-y^2 + 16\cdot y + 1)/7 |
7,758 | 2*x + (-1) < x + 1 \implies x \lt 2 |
3,958 | \frac{2}{24} = \frac{1}{15 + 2 + 7} \cdot 2 |
41,284 | \frac{1}{5} 3 = \dfrac15 3 |
13,607 | \frac{1}{\cos(h)}*\sin(h) = \tan(h) |
-14,069 | 6 + (9 \times 4) = 6 + (36) = 6 + 36 = 42 |
-3,470 | \dfrac{5\cdot 9}{20\cdot 5} = 45/100 |
-23,084 | 2(-\frac23) = -4/3 |
5,795 | n\cdot 2^{n + (-1)} = (\sum_{k=0}^n \binom{n}{k}) k = (\sum_{k=1}^n \binom{n}{k}) k |
-6,483 | \tfrac{2\cdot q}{(\left(-1\right) + q)\cdot \left(7\cdot (-1) + q\right)} = \dfrac{2\cdot q}{7 + q^2 - q\cdot 8} |
-29,363 | (y + 4) (y + 6) = y^2 + 6 y + 4 y + 24 = y^2 + 10 y + 24 |
18,811 | \frac1x \times x^3 = r \implies r = x^2 |
14,336 | -x^2 + d^2 = (-x + d) \cdot (x + d) |
24,703 | y^{12} + (-1) = ((-1) + y^6)*(y^6 + 1) |
-20,056 | \frac19\cdot 9\cdot \frac{1}{i\cdot (-9)}\cdot (1 + 5\cdot i) = \frac{9 + 45\cdot i}{i\cdot (-81)} |
4,151 | 3 \cdot h \geq 0 \implies h = |h| |
8,985 | \frac{1}{R \cdot U} = \frac{1}{R \cdot U} |
-22,224 | x^2 + 9x + 20 = (x + 5) (4 + x) |
-20,268 | \frac{8\cdot q}{q\cdot 72} = 8\cdot q\cdot 1/(8\cdot q)/9 |
30,309 | 2^{n + (-1)}\cdot (2^n + 1 + 2\cdot (-1)) + (-1) = 2^{n + (-1)}\cdot (2^n + 1) - 2^n + \left(-1\right) = (2^n + 1)\cdot (2^{n + (-1)} + \left(-1\right)) |
47,507 | \frac{\mathrm{d}z}{\mathrm{d}x} = \frac{-h_x + h/g \cdot g_x}{h_z - \frac{h}{g} \cdot g_z} = \frac{-g \cdot h_x + h \cdot g_x}{g \cdot h_z - h \cdot g_z} |
-3,178 | -\sqrt{9} \sqrt{7} + \sqrt{16} \sqrt{7} = \sqrt{7}\cdot 4 - \sqrt{7}\cdot 3 |
11,321 | \frac{1}{2 \cdot (-1) + 5^{1/2}} = \frac{\frac{1}{5^{1/2} + 2}}{5^{1/2} + 2 \cdot (-1)} \cdot (2 + 5^{1/2}) |
53,472 | 16 \cdot 16 = 256 |
4,433 | \frac{\frac{1}{4}}{1 - \frac{1}{4}} = \frac13 |
-2,529 | 2\sqrt{5} = ((-1) + 3) \sqrt{5} |
19,240 | 3/2 - \dfrac23 = 5(\frac{1}{2} - \dfrac{1}{3}) |
14,804 | 1/9 + \frac{4*\frac13}{18} = \frac{1}{27}*5 |
21,902 | 30^{2010} \cdot 67^{2011} = \left(30 \cdot 67\right)^{2010} \cdot 67 |
15,396 | |A^\complement \cap E^\complement| = |D \backslash A \cup E| = |D| - |A| - |E| + |A \cap E| |
-13,251 | 9 \times (1 + 2) = 9 \times 3 = 27 |
14,920 | -x \cdot 2 = d/dx \left(-x^2\right) |
6,888 | 2/3 = \dfrac{\frac{2}{9}}{\dfrac13} \cdot 1 |
12,495 | e^{F + x} = e^F \times e^x = e^x \times e^F |
32,407 | 0 = s^2 - x \cdot s - x \Rightarrow \dfrac{1}{2} \cdot (x \pm \sqrt{x^2 + 4 \cdot x}) = s |
28,091 | \sin(D + G) = \cos{D} \times \sin{G} + \cos{G} \times \sin{D} |
2,103 | x^5 + x + (-1) = x^5 + x^2 - x^2 + x + \left(-1\right) = (x^2 - x + 1) (x^3 + x^2 + (-1)) |
7,042 | 1/N = \frac{1}{N \cdot N}\cdot N |
-6,730 | \frac{1}{10}3 + 3/100 = \frac{30}{100} + \frac{3}{100} |
23,967 | 1 + 2m - q + 1 = 2m - q |
-2,014 | 13/12\cdot \pi - \pi/6 = \dfrac{11}{12}\cdot \pi |
-1,950 | 5/3 \cdot \pi + \frac{17}{12} \cdot \pi = \pi \cdot 37/12 |
1,460 | \frac{1}{n^2} \times (n + (-1)) \times (1 + n) = 1 - \dfrac{1}{n^2} |
26,709 | -(-z + m)^2 + (m + z)^2 = z \cdot m \cdot 4 |
-25,801 | \frac{5*1/6}{3} = \frac{5}{18} |
8,471 | -(-y^2 + A \cdot A) \cdot \sqrt{-y^2 + A^2}/3 + Z = Z - (A^2 - y^2)^{\frac12 \cdot 3}/3 |
-6,695 | 3/100 + 5/10 = 3/100 + \frac{50}{100} |
-12,751 | \dfrac36 = \dfrac{1}{2} |
16,840 | q^2\cdot (\left(-1\right) + q)/2 = (-q^2 + q^3)/2 |
16,617 | \cos^2(x) \cdot 2 = -2\sin^2(x) + 2 |
26,532 | 24/(\sqrt{6}) = \sqrt{6}/\left(\sqrt{6}\right)\cdot \frac{1}{\sqrt{6}}\cdot 24 |
-16,780 | {-4k} = ({-4k} \times -2k) + ({-4k} \times 6) = (8k^{2}) + (-24k) = 8k^{2} - 24k |
15,389 | \tfrac{1}{f + d}*(f^2 - d^2) = f - d |
-9,935 | -0.88 = -\tfrac{22}{25} |
29,323 | 14 = 27 + 13\cdot \left(-1\right) |
-25,825 | \frac{5\cdot 1/4}{7\cdot 1/5} = 5/4\cdot \tfrac17\cdot 5 = \frac{5\cdot 5}{4\cdot 7} = 25/28 |
10,955 | 1 - \frac{2}{15} = \dfrac{13}{15} |
1,188 | l \cdot l \cdot l + 3 \cdot (-1) = \frac{1}{2} \cdot l^3 + \dfrac12 \cdot l^2 \cdot l + 3 \cdot (-1) > \frac{1}{2} \cdot l^2 \cdot l |
32,210 | {n + 1 \choose n} + 1 = {n + 2 \choose 1 + n} |
11,966 | 0 = s^2 - s \implies s = 0,1 |
12,452 | z^2 = -y^2 + 2 - z \cdot z \Rightarrow 1 = z^2 + y^2/2 |
25,899 | \dfrac16\cdot 312 = 52 |
34,924 | \delta_{x_i} = \frac12\cdot \delta_{x_i} |
751 | (2^{(-1) + l} + (-1)) \cdot (1 + 2^l) = (-1) + {2^l \choose 2} |
11,163 | (1 + x) \cdot (x + (-1)) = (-1) + x \cdot x |
48,313 | {1 + 5 \choose 1} = {6 \choose 1} |
30,668 | 0.6*(\left(-1\right)*0.4 + 1)*\left((-1)*0.2 + 1\right) = 0.288 |
326 | -\tfrac{2}{4^{1/2}} = -\tfrac{1}{2}2 = -1 |
19,682 | 2*\dfrac{1}{(2*y)^2 + 1}/3 = d/dy (\operatorname{atan}\left(y*2\right)/3) |
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