This demo shows a comparison between the neural model (i.e., Transformer) and the neural-symbolic model by abductive learning (i.e., Abl-Sym).
The models are both learned from the DeepMind math dataset (examples shown in the right panel). Details described in the paper
Yangyang Hu and Yang Yu. Enhancing neural mathematical reasoning by abductive combination with symbolic library. https://arxiv.org/abs/2203.14487 (code)
Answer by Abl-Sym
''
Answer by Transformer
''
Examples
Solve -q = -28 + 27 for q.
Let b(w) = -w**3 + 7*w**2 + 10*w - 7. Let p be b(8). Solve -4*a - p = -a for a.
Put together 2313 and -1740.
In base 13, what is -5bb + -5?
(-6 - -5) + (-1 - 0) - 1
38 divided by -5
-1 - ((-24)/(-6) - -4)
Product of 139 and 24.
What is ((-9)/15)/((-2)/10)?
What is the square root of 27255 to the nearest integer?
Simplify (sqrt(110) + -1*sqrt(110)*-6)/sqrt(10).
What is the third derivative of 2*a*n*s**3 - a*n*s**2*y + 2*a*n*s*y - a*s**3*y + 2*a*s**2*y + n*s**3 + 18*n*s**2 + 91*s**3*y wrt s?
Let m(z) be the first derivative of z**6/40 - z**4/6 + z**2 + 5. Let t(j) be the second derivative of m(j). What is the second derivative of t(v) wrt v?
Which is the nearest to -6/5? (a) -2 (b) 3 (c) 18.1
Let x be 4/(-30)*(21/12 + -3). Which is the closest to 2/5? (a) -2 (b) x (c) 5
How many millilitres are there in 3/10 of a litre?
How many minutes are there between 5:28 AM and 2:37 PM?
Convert 11 (base 4) to base 6.
Calculate the remainder when 3641 is divided by 8.
Let g(z) = 2*z - 5. What is the remainder when 13 is divided by g(5)?
What is the greatest common divisor of 38 and 608?
Suppose 20 = 3*w - 8*w. Let k be 11*2*6/w. Let t be (-6)/(-3) + -1 - k. Calculate the greatest common divisor of 85 and t.
Is 3046 a multiple of 54?
Suppose 0*z = 5*z + 115. Let b = -8 - z. Let w = b - -19. Is w a multiple of 17?
Is 12677 prime?
Suppose o + u - 84 = 133, -5*o + 1087 = 3*u. Suppose -o = -5*l - 33. Is l prime?
Calculate the smallest common multiple of 28 and 156.
Calculate the least common multiple of 1 and (-1)/3 + (-96)/(-18).
List the prime factors of 73689.
Let v be 23/3 + 4/12. Suppose h + 4*t + v = -8, -5*t - 20 = 3*h. What are the prime factors of (9 - (h - 2)) + 1?
What is the hundreds digit of 1062?
Suppose -5*p - 16 = 4*s, 3*s - 2*p = -0*p - 12. What is the tens digit of 10 - (s - -2)/1?
What is 0.54731 rounded to two dps?
Let y = 267.0000234 - 267. What is y rounded to 6 dps?
Let q(f) = -4*f**3 + 12*f**2. Let k(o) = -o**2. Give -10*k(p) - q(p).
Express -2*b**2 - 4*b**4 + 4*b**3 - 2*b + 2*b**4 + 10 + 4*b**4 - 15 as r + z*b**3 + i*b + d*b**2 + l*b**4 and give r.
Collect the terms in -3*q**2 + 2*q**2 + 0*q - 2*q + 2*q**2.
Let j(u) = -13*u. Let t(i) = -3*i. Let c(y) = y. Let m(s) = -5*c(s) - 2*t(s). What is m(j(l))?
Let l(h) = 2*h**2 - 10*h + 6. Determine l(4).
Let s = 8 - 8. Let v(t) = -2*t**2 + 1 + 0*t + 1 + s*t + 2*t. Calculate v(3).
Expand 10*l**3 + 4*l**3 - 4*l**3 - 2*l**3 - l**3 + l**3 + (2*l**2 + l - l)*(-l - 1 + 1) - l + l**3 + l.
Simplify (o*o*o/(o**(-3)*o))/(((o*o**(-7)*o*o*o*o*o)/o)/o)*(o/(o/(o*o*o**(-5)/o)))/(o/(o**(2/25)*o)) assuming o is positive.
Calculate prob of picking 3 s and 1 l when four letters picked without replacement from mslllhmlmss.
Calculate prob of sequence qmj when three letters picked without replacement from {m: 8, j: 2, k: 2, q: 2}.