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int64 -30,985
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-4,415 | 4 + x^2 + x*5 = (x + 1)*(x + 4) |
3,403 | x^2 + z * z = (x - t + t)^2 + z^2 = (x - t)^2 + 2*(x - t)*t + t * t + z^2 |
2,365 | z_x = z \cdot z_x/z |
-9,833 | 0.01 (-20) = -20/100 = -\dfrac15 |
15,032 | (y^2 \times x + y \times z \times z + z \times x^2)/2 + 3 = (y \times x \times y + z \times y \times z + x \times z \times x)/2 + 3 |
9,792 | An = 1 + 7/10 (An - A) + \frac{3}{10} (An + A) = An + 1 - \dfrac25 A |
36,054 | 30^{1 / 2}\cdot 2/5 = 30^{\frac{1}{2}}\cdot 2/5 |
-13,688 | 5 + (6 - 8 \cdot 8) = 5 + (6 + 64 \cdot (-1)) = 5 - 58 = 5 + 58 \cdot \left(-1\right) = -53 |
-4,279 | \frac{k^3 \cdot 2}{5 \cdot k^2} = \tfrac25 \cdot \frac{1}{k \cdot k} \cdot k^3 |
23,980 | \pi\cdot 3/4 = \pi - \tfrac{1}{4}\pi |
17,490 | -16 t^2 + 32 t + 20 = -(-5/4 + t^2 - 2t)*16 |
8,095 | -\frac{64}{-8} + 15 = 15 - 4^3/\left(-8\right) |
3,280 | 2 \cdot \sqrt{3} + 4 = 3 + \sqrt{3} \cdot 2 + 1 |
24,224 | A_m^F A_{(-1) + m}^F \dots A_1^F A_2^F = (A_1 A_2 \dots A_m A_{(-1) + m})^F |
23,928 | 1/A + A = 2 \cdot x \implies x \pm (x^2 + (-1))^{1 / 2} = A |
16,869 | j_1 \cdot c_1 = c \cdot j \implies j/(j_1) \cdot c = c_1 |
-1,248 | 5/6*(-\dfrac{4}{3}) = (\frac{1}{3}*\left(-4\right))/(\frac{1}{5}*6) |
4,209 | 10 = 2 \cdot 5 = \sqrt{10} \cdot \sqrt{10} |
15,355 | \frac{1}{u^2 + (-1)} = \frac{1}{((-1) + u) \cdot (u + 1)} |
23,454 | y = \frac{1}{2}y + y/2 |
28,461 | 26 = 5^2 + 1^2 = 4^2 + 3^2 + 1 1 = 3^2 + 3^2 + 2^2 + 2^2 |
18,218 | 1 - e + 2 - e = 0\Longrightarrow e = 1.5 |
698 | \dfrac13 \cdot 0 + \frac{2}{3} \cdot (\frac12 + 1/2) = \dfrac{2}{3} |
-18,962 | 1/3 = \dfrac{1}{25\cdot \pi}\cdot A_s\cdot 25\cdot \pi = A_s |
-2,986 | (25*10)^{1/2} - 10^{1/2} = 250^{1/2} - 10^{1/2} |
17,877 | \left(x = -a \Rightarrow x^m = a^m\right) \Rightarrow a^m + x^m = a^m \cdot 2 |
-12,184 | \frac38 = p/(8 \pi)*8 \pi = p |
20,923 | 2*\sin(5*z)*\cos(4*z) = \sin\left(5*z + 4*z\right) + \sin(5*z - 4*z) = \sin(9*z) + \sin(z) |
12,947 | \frac{30*7!}{9!} = \frac{30}{72} = 5/12 |
1,398 | \frac{g^2 c^2}{x g + x c} = \frac{x^2 c^2}{x g + g c} = \tfrac{x^2 g g}{g c + x c} |
8,272 | \frac{i}{1 + i^2\cdot x^2} = \frac{\partial}{\partial x} \arctan(x\cdot i) |
10,266 | \binom{3 \cdot (-1) + n + r}{r} = \binom{(-1) + n + 2 \cdot (-1) + r}{r} |
5,370 | \dfrac{(k_A \cdot L)^9}{(k_A \cdot L)^5} = (k_A \cdot L)^4 |
29,645 | -1 = \sin{\dfrac{3\cdot \pi}{2}\cdot 1} |
-20,836 | \frac{(-12) k}{9(-1) + k*3} = 3/3 \frac{\left(-1\right)*4 k}{k + 3(-1)} |
11,418 | 1.44\cdot x = (1 + 0.2)^2\cdot x |
-2,826 | (1 + 3) \cdot 2^{1 / 2} = 4 \cdot 2^{1 / 2} |
15,936 | (t - -3)\cdot (3\cdot (-1) + t) = (3 + t)\cdot (t + 3\cdot \left(-1\right)) |
13,188 | (z - 3i) (-3i + z) = i*3*i*3 + zz - i*3 z - z*3i |
-624 | \frac{1}{4}\pi = -14 \pi + \pi \frac{57}{4} |
3,164 | (x - k + 1)! = (-k + x)! (1 + x - k) |
31,191 | h\cdot g = -g\cdot \left(-h\right) |
20,618 | 36^{-\frac12*5} = (6^2)^{-\frac{1}{2}*5} = 1/7776 |
-1,340 | 1/4*5/((-1)*8*\tfrac19) = 5/4 \left(-\frac{9}{8}\right) |
-20,564 | -\frac{9}{1} \frac{-z \cdot 6 + 4}{-z \cdot 6 + 4} = \frac{z \cdot 54 + 36 (-1)}{4 - 6z} |
-428 | \frac{19}{12}\cdot \pi = \frac{115}{12}\cdot \pi - 8\cdot \pi |
20,314 | 2x x^4*9 + x^5*6 + 4x^3*5x^2 = x^5*44 |
18,355 | 2*32*4^4 + 4^4*8*28 = 73728 |
13,850 | A^2 + A - I_2 = t*A - I_2 + A - I_2 = (t + 1)*A - 2*I_2 |
-3,060 | \sqrt{4} \sqrt{11} + \sqrt{11} = \sqrt{11} + \sqrt{11}\cdot 2 |
8,360 | z^2 + z\cdot p + q = -p^2/4 + (z + \frac{p}{2})^2 + q |
18,366 | 15 = (5 + 2 (-1))^2 + 6 |
33,589 | (z + 1) \times g + (z + 1) \times f = (1 + z) \times (f + g) |
-20,060 | -5/3*\frac{2*(-1) - y*6}{-y*6 + 2*(-1)} = \frac{y*30 + 10}{-y*18 + 6*\left(-1\right)} |
13,297 | \frac{\binom{48}{3}}{\binom{52}{3}}\cdot \binom{4}{0} = \binom{48}{3}/\left(\binom{52}{3}\right) |
19,754 | \left(4k \cdot 3 = 4 \cdot (24 - y) \Rightarrow k \cdot 3 = 24 - y\right) \Rightarrow y = 24 - k \cdot 3 |
-13,752 | \frac{70}{8 + 6} = \dfrac{70}{14} = \dfrac{70}{14} = 5 |
-23,492 | 1/6 = \frac{1}{9} \cdot 4 \cdot 3/8 |
-9,239 | -11\cdot 2\cdot 2\cdot 2 - 3\cdot 11 p = 88 \left(-1\right) - 33 p |
148 | \left(x^{14} + x^{10} + x^6\right) \cdot (-x + x^5) = x^{19} - x^7 |
3,532 | -35/2 + z^2 + 3/2\cdot z = (2\cdot z + 7\cdot (-1))\cdot (5 + z)/2 |
7,434 | x x x = \left(x + (-1) + 1\right)^3 = (x + (-1))^3 + 3 \left(x + (-1)\right)^2 + 3 \left(x + \left(-1\right)\right) + 1 |
12,073 | 243/2 = 729/4 - \dfrac{729}{12} |
7,543 | \tan{50} = \tan(45 + 5) = \frac{1}{1 - \tan{45} \tan{5}} (\tan{45} + \tan{5}) |
19,232 | 10^{\left(n + 1\right)^2} = 10^{n^2 + 2 n + 1} = 10^{n n}\cdot 10^{2 n}\cdot 10^1 |
25,030 | |x + 2 (-1)| = |x + (-1) + (-1)| \leq |x + (-1)| + 1 |
8,128 | 2 + 3*n = 5 + \left(\left(-1\right) + n\right)*3 |
10,693 | \frac{\sin{-x}}{x \cdot (-1)} = \dfrac{1}{x} \cdot \sin{x} |
14,638 | l^{f + g} = l^g l^f |
-12,427 | 48 = 66 \cdot (-1) + 114 |
33,344 | \frac{\partial}{\partial x} (\tfrac{1}{m!}*x^m) = \frac{1}{m!}*m*x^{m + \left(-1\right)} = \frac{x^{m + (-1)}}{(m + (-1))!} |
-1,924 | \frac12 \cdot \pi - \pi \cdot \dfrac{17}{12} = -\pi \cdot 11/12 |
19,309 | 1 + \frac{1}{z + (-1)} = \dfrac{z + (-1) + 1}{z + (-1)} = \dfrac{1}{z + (-1)}*z |
36,774 | 310 = 31/2\cdot \left(2\cdot b_1 + 30\cdot g\right) = 31\cdot (b_1 + 15\cdot g) |
15,133 | \frac{1}{2} \cdot (q^m + (-1)) = \frac{(q^m + (-1)) \cdot (\left(-1\right) + q)}{(q + (-1)) \cdot 2} |
-18,391 | \tfrac{1}{(j + 7) \cdot j} \cdot (6 + j) \cdot (7 + j) = \frac{1}{j^2 + j \cdot 7} \cdot \left(j^2 + 13 \cdot j + 42\right) |
23,782 | (-f - f)/(2\cdot g) = ((-2)\cdot f)/\left(2\cdot g\right) = \dfrac1g\cdot ((-1)\cdot f) |
6,807 | \sin(2\cdot v) = 2\cdot \sin(v)\cdot \cos\left(v\right) |
8,779 | m^4\cdot 4 + z^4 = (z^2 - 2\cdot z\cdot m + 2\cdot m^2)\cdot (z^2 + z\cdot m\cdot 2 + 2\cdot m^2) |
-6,170 | \frac{p}{(4 + p) \cdot (p + 1)} = \dfrac{1}{4 + p^2 + 5 \cdot p} \cdot p |
17,758 | k + z^2 = 0 \Rightarrow (-k)^{1/2} = z |
7,983 | \frac{b}{h}\cdot 8 = 8/(\frac{1}{b}\cdot h) |
5,985 | (x*x^Z)^Z = (x^Z)^Z*x^Z = x*x^Z |
-4,613 | \dfrac{-x \cdot 2 + 7 \cdot (-1)}{20 + x^2 + x \cdot 9} = \tfrac{1}{x + 4} - \frac{3}{x + 5} |
17,361 | \left(x \cdot h\right) \cdot \left(x \cdot h\right) \cdot \left(x \cdot h\right) = h^3 \cdot x^2 \cdot x |
-20,672 | (-9t + 24 (-1))/(-6) = \dfrac{1}{-2}(-t\cdot 3 + 8\left(-1\right))\cdot 3/3 |
22,392 | \left(0 + a\right)^2 = 0^0 a \cdot a + 2 \cdot 0^1 a^1 + 0^2 a^2 = 0^0 a^2 |
12,560 | b^3 + 3\times b^2 + 5\times b + 5 = 2 + (1 + b)^3 + (b + 1)\times 2 |
5,923 | \frac{x^2*2}{x * x + 1} = 2 - \frac{2}{x^2 + 1} |
-2,252 | \frac{1}{20} \cdot 7 = -2/20 + 9/20 |
26,051 | \cot^2{x} + 1 = \dfrac{1}{\sin^2{x}} |
4,279 | G = I*G = G*I |
25,229 | \frac{3 \cdot 1/8}{\frac38 + \frac{6}{10}} = 5/13 |
16,142 | \sin{x\cdot 2} = -\sin{v} \implies \arcsin(-\sin{v}) = 2\cdot x |
138 | \cos(g + a) = \cos{a} \cos{g} - \sin{a} \sin{g} |
-27,725 | -\cot(y)\cdot \csc(y) = d/dy \csc(y) |
54,113 | \sum_{m=1}^\infty \frac{m}{y^m} = \sum_{m=1}^\infty -y\cdot \frac{\partial}{\partial y} \frac{1}{y^m} = -y\cdot \frac{\partial}{\partial y} \sum_{m=1}^\infty \frac{1}{y^m} |
31,112 | \frac1b = \frac{b}{b\cdot b} = \frac{b}{b^2} = \frac{b}{|b|^2} |
26,103 | \dfrac{a}{(b - c)*y*z}*h*x = \frac{b*h*y}{(c - a)*x*z}*1 = \frac{c*h*z}{(a - b)*x*y} |
26,023 | 6 = \frac{1}{2}\cdot \left(16 + 4\cdot (-1)\right) |
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