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int64 -30,985
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-18,972 | \dfrac{1}{15}8 = \dfrac{C_p}{4\pi} \cdot 4\pi = C_p |
-25,055 | \dfrac{2*10^{-1}}{9} = 2/90 = 1/45 |
404 | 1 + 5^{1/2} = \left(x + h\cdot 5^{1/2}\right)\cdot (s + f\cdot 5^{1/2}) = x\cdot s + 5\cdot h\cdot f |
-20,985 | \frac{1}{9}\cdot 9\cdot \dfrac{1}{7\cdot (-1) + a}\cdot ((-1) + a) = \frac{9\cdot a + 9\cdot (-1)}{a\cdot 9 + 63\cdot (-1)} |
-3,401 | -3^{\frac{1}{2}} + (16*3)^{1 / 2} = -3^{1 / 2} + 48^{\frac{1}{2}} |
-12,362 | 75 = 5 \cdot 5 \cdot 3 |
26,715 | 1 + x^3 = \left(x + 1\right)*\left(1 + x^2 - x\right) |
29,120 | 4/81 = 16\cdot 1/81/4 |
32,516 | \frac{1}{12} + 1/2 + 1/4 + 1/6 = 1 |
14,727 | x^6 + x^4 + x \cdot x \cdot x - x^2 + (-1) = (2 + x^2 - x)\cdot (x^4 + x^3 + (-1)) - x^3 - x + 1 |
25,825 | \mathbb{E}(\left(B - \mathbb{E}(B)\right)^2) = -\mathbb{E}(B)^2 + \mathbb{E}(B \times B) |
36,725 | -\sin(x) \cdot ((-1) + \cos^2(x)) = \sin^3(x) |
16,662 | 4\cdot (2\cdot \cos^2{x})^2 = 4\cdot (\cos{2\cdot x} + 1) \cdot (\cos{2\cdot x} + 1) = 4\cdot \cos^{22}{x} + 8\cdot \cos{2\cdot x} + 4 |
-9,383 | l*21 = 3*7*l |
28,917 | \frac15 3 - \frac{1}{5} 3 = 0 |
7,270 | -\left(1/4 + 1/2\right)\times \dfrac{1}{2}\times \frac{1}{2}\times 1/2 + 1 = \frac{29}{32} |
2,889 | \frac{8}{9} = 1 - \dfrac19 |
1,186 | (2\cdot \dfrac{1}{3})^2 + (2\cdot 2/3)^2 = 20/9 > 2 |
-10,267 | -\frac{45\cdot x + 45\cdot \left(-1\right)}{60\cdot (-1) + 15\cdot x} = 15/15\cdot (-\frac{1}{4\cdot \left(-1\right) + x}\cdot (3\cdot x + 3\cdot \left(-1\right))) |
12,471 | \tfrac{\sin\left(\pi/x\right)}{x^2} \cdot \pi = \frac{\mathrm{d}}{\mathrm{d}x} \cos(\frac{\pi}{x}) |
8,947 | \operatorname{Var}(-R) = \operatorname{Var}(R) |
19,495 | \frac{f}{g} - h \cdot g/g = \frac{1}{g} \cdot (f - h \cdot g) |
-13,692 | 6 - 3 \cdot 8 + \frac{48}{6} = 6 - 3 \cdot 8 + 8 = 6 + 24 \cdot (-1) + 8 = -18 + 8 = -10 |
-20,716 | \dfrac{1}{p*\left(-8\right)}*p*14 = -\dfrac{7}{4}*\dfrac{1}{\left(-2\right)*p}*(\left(-2\right)*p) |
20,313 | (2^m + \left(-1\right)) \cdot \left(2^m + 1\right) = 4^m + (-1) |
32,259 | a^m = a \times a^{m + (-1)} = a^{m + \left(-1\right)} \times a |
29,839 | 6*5*21^5 = 122523030 |
-13,895 | \dfrac{ -10 }{ (9 - 10) } = \dfrac{ -10 }{ (-1) } = \dfrac{ -10 }{ -1 } = 10 |
-20,892 | -6/5\cdot \dfrac{1}{5}5 = -\frac{1}{25}30 |
7,873 | \cos{\psi_2} = \cos{\psi_1} \Rightarrow \psi_1 = \psi_2 |
33,245 | q^3 + r^3 + 6 \cdot q \cdot r = q^3 + r^3 + 3 \cdot (q + r) \cdot q \cdot r + \left(6 - 3 \cdot q - 3 \cdot r\right) \cdot q \cdot r = (\dfrac12 \cdot 3)^3 + \tfrac32 \cdot q \cdot r |
2,221 | xt \cdot 2 + p^2 + x^2 + t^2 + 2xp + 2tp = (p + x + t)^2 |
8,396 | j\cdot x = x\cdot j |
38,634 | X = X\cdot π/π |
22,841 | A \cdot 7 = A \cdot 4 + A + 2 \cdot A |
18,129 | \frac{1^{-1}}{3^4}\cdot 1^{-1} = \frac{1}{3^4}\cdot 1 = \frac{1}{3^4}\cdot 1^{-1} = \frac{1}{3^4} = \frac{1}{81} |
23,586 | (3 \cdot x + x) \cdot 3 = x \cdot 12 |
-29,471 | -8 + \dfrac{70}{-7} = -8 - 10 = -18 |
-24,721 | \frac{1}{k^2 + 16 \cdot (-1)} \cdot \left(2 \cdot (-1) + k \cdot 2\right) + \dfrac{1}{16 \cdot \left(-1\right) + k^2} \cdot (-k + 6) = \tfrac{4 + k}{16 \cdot (-1) + k \cdot k} |
41,013 | \left(-1\right) + 1024 + 32 + 8 = 1063 |
5,498 | -t/3 + t = \frac{1}{3} \cdot 2 \cdot t |
12,294 | \frac12 \cdot (f + b) = \frac12 \cdot (2 \cdot f + b - f) = f + (b - f)/2 |
16,962 | 50*\sqrt{3} = A + 0*\left(-32\right) rightarrow A = 50*\sqrt{3} |
17,443 | 0 = 0\cdot w = (1 - 1)\cdot w = w - w |
10,075 | 10^6/(\binom{60}{6}) = \frac{1000000}{50063860} = 0.1997 |
2,965 | 51^2 - 2 \times 10 \times 10 = 2401 |
-4,463 | \frac{3}{x + 5} - \frac{1}{x + 2 \cdot (-1)} \cdot 2 = \frac{16 \cdot (-1) + x}{10 \cdot \left(-1\right) + x^2 + 3 \cdot x} |
-9,589 | -\frac{4}{25} = -0.16 |
17,458 | (y + x)^2 = x^2 + 2\cdot x\cdot y + y^2 |
-2,962 | 2^{\frac{1}{2}} \cdot (5 \cdot (-1) + 2 + 4) = 2^{1 / 2} |
-26,478 | 3\cdot \left(16 - y\cdot 8 + y^2\right) = 3\cdot y^2 + 48 - y\cdot 24 |
14,025 | 7 \cdot {7 + n \choose n} = {6 + n \choose n} \cdot (7 + n) |
10,388 | \frac{3^3}{3} + 3^2 + \frac{2(3)}{3} = 20 |
13,925 | -e^{x*3} + \frac{\mathrm{d}15}{\mathrm{d}x} = -3*e^{x*3} |
-30,970 | 60 s = 60 s |
-11,594 | -i \cdot 9 + 6 + 0 \cdot (-1) = 6 - 9 \cdot i |
-15,810 | 9/10\cdot 5 - 8/10 = \frac{37}{10} |
10,514 | 13 + 2\cdot l + 1 = \left(l + 7\right)\cdot 2 |
47,534 | \frac{r}{2 - r} + (1 - r)\times \left(1 - \dfrac{1}{2 - r}\right) = \frac{1}{2 - r}\times (r + (1 - r)\times \left(1 - r\right)) = \frac{1}{2 - r}\times (1 - r + r^2) |
31,349 | x^2 + 3 \cdot x + 10 \cdot (-1) = \left(x + 2 \cdot (-1)\right)^2 + 7 \cdot x + 14 \cdot \left(-1\right) = (x + 2 \cdot (-1))^2 + 7 \cdot x + 14 \cdot (-1) = (x + 2 \cdot (-1))^2 + 7 \cdot (x + 2 \cdot (-1)) |
26,156 | 780 = 780 + 17 \cdot 0 |
22,598 | -\frac{1}{2378} \cdot 5 = -\tfrac{5}{2378} |
42,938 | \frac{100}{0.625} = 160 |
691 | 495 - 5*\binom{7}{3} + \binom{5}{3}*7 + \binom{7}{4} + \binom{5}{4} = 210 |
12,243 | -b^{1 + n} + a^{n + 1} = (a - b) \cdot (a^n + a^{(-1) + n} \cdot b + \dots + b^{(-1) + n} \cdot a + b^n) |
17,750 | x^2 - 6x = (x + 3(-1))^2 + 9(-1) |
31,110 | f_2 + f_1 + m = m + f_2 + f_1 |
-24,193 | \dfrac{44}{6 + 5} = \dfrac{44}{11} = 44/11 = 4 |
-7,235 | 1/9 = \frac{2}{6}*1/3 |
2,393 | {1 \choose 1} \cdot {3 \choose 2} \cdot {5 \choose 2} \cdot {7 \choose 2} = \frac{1}{2! \cdot 1! \cdot 2! \cdot 2!} \cdot 7! |
19,870 | \dfrac{1/D\cdot \frac{1}{C}}{D^T} = \dfrac{1}{D\cdot D^T\cdot C} |
2,677 | c_1\cdot c_2^i = c_1\cdot c_2^i |
21,757 | z \cdot z + 0\cdot z + 0 = z^2 |
463 | (Z + 1)\times \left((-1) + Z\right) = \left(-1\right) + Z^2 |
-15,593 | \frac{1}{p_2^3 \cdot \frac{1}{\dfrac{1}{p_2^8} \cdot \dfrac{1}{p_1^8}}} = \frac{1}{p_2^8 \cdot p_1^8 \cdot p_2^3} |
-2,879 | 5 \cdot 5^{1/2} + 5^{1/2} \cdot 4 = 16^{1/2} \cdot 5^{1/2} + 25^{1/2} \cdot 5^{1/2} |
13,209 | x_t + x_q = x_t - x_q + x_q + x_q = x_t - x_q + 2x_q |
-341 | \frac{6! \cdot 1/3!}{1/6! \cdot 9!} = \tfrac{6! \cdot \frac{1}{3! \cdot (6 + 3 \cdot (-1))!}}{\tfrac{1}{3! \cdot \left(9 + 3 \cdot (-1)\right)!} \cdot 9!} |
22,600 | \frac13\cdot (1 + L) = L \implies L = 1/2 |
27,310 | i!*\left(i + 1\right) = (1 + i)! |
7,569 | |(y + \left(-1\right))*(2*(y + 1) + 3) + 3| = \cdots = |\left(y + (-1)\right)*(2*y + 5) + 3| = |\left(y + (-1)\right)*(2*y + 2*\left(-1\right) + 7) + 3| = |y + (-1)|*(2*|y + \left(-1\right)| + 7) + 3 |
12,380 | \pi = x*2 \implies \pi/2 = x |
18,114 | \frac13 = \dfrac{10}{30} |
13,974 | A + B + C = 0 \Rightarrow \sin(A + B) = \sin(-C) = -\sin\left(C\right), \cos\left(A + B\right) = \cdots = \cos(C) |
21,580 | x + \left(-1\right) + x + \left(-1\right) = 2 \cdot x + 2 \cdot (-1) \gt x |
50,794 | 1 = \frac{1}{2} + \frac12 |
8,805 | X_{2 \cdot r} - X_r - -X_w + X_{2 \cdot w} = -(X_r - X_w) + X_{r \cdot 2} - X_{w \cdot 2} |
22,620 | (-c + a) \cdot (a^{n + (-1)} + c \cdot a^{2 \cdot (-1) + n} + a^{n + 3 \cdot \left(-1\right)} \cdot c \cdot c + ... + c^{3 \cdot (-1) + n} \cdot a^2 + c^{n + 2 \cdot (-1)} \cdot a + c^{(-1) + n}) = a^n - c^n |
10,990 | \pi/2 + l\pi*2 = \pi*(1 + l*4)/2 |
43,769 | 11^3*7*13 = 121121 |
-20,997 | 4/4\cdot \frac{-r + 3\cdot (-1)}{r\cdot 2} = (12\cdot (-1) - r\cdot 4)/(r\cdot 8) |
3,328 | (xy)^2 = y \cdot y x^2 |
523 | \cos(2q) = 1 - 2\sin^2(q) |
2,681 | \binom{m + (-1)}{0} = \binom{m}{0} |
-20,012 | \frac{k\cdot 3 + 5}{k\cdot 3 + 5}\cdot 5/8 = \frac{25 + 15\cdot k}{k\cdot 24 + 40} |
35,998 | \binom{l - 1/2}{l} = (-1)^l\cdot \frac{\binom{2\cdot l}{l}}{4^l} \approx \frac{1}{\sqrt{\pi\cdot l}}\cdot (-1)^l |
17,325 | x\times 2 = \frac{d}{dx} x^2 |
-23,829 | 10 + \frac{1}{10}90 = 10 + 9 = 10 + 9 = 19 |
-5,741 | \frac{1}{q \cdot q - q \cdot 10 + 9} \cdot 3 \cdot q = \tfrac{3 \cdot q}{\left(9 \cdot (-1) + q\right) \cdot \left(q + (-1)\right)} |
12,155 | (m + (-1)) * (m + (-1)) = 1 + m * m - 2m |
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