added formula table

README.md

@@ -49,16 +49,59 @@ task_ids: []
 ## Dataset Description
 
 - **Homepage:**
-- **Repository:**
+- **Repository:** https://github.com/omron-sinicx/srsd-benchmark
 - **Paper:** Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery
-- **Point of Contact:**
+- **Point of Contact:** [Yoshitomo Matsubara](mailto:yoshitom@uci.edu) [Yoshitaka Ushiku](mailto:yoshitaka.ushiku@sinicx.com)
 
 ### Dataset Summary
 
 Our SRSD (Feynman) datasets are designed to discuss the performance of Symbolic Regression for Scientific Discovery.
 We carefully reviewed the properties of each formula and its variables in [the Feynman Symbolic Regression Database](https://space.mit.edu/home/tegmark/aifeynman.html) to design reasonably realistic sampling range of values so that our SRSD datasets can be used for evaluating the potential of SRSD such as whether or not a SR method con (re)discover physical laws from such datasets.
 
-This is the Medium set of our SRSD-Feynman datasets, which consists of 40 different physics formulas.
+This is the Medium set of our SRSD-Feynman datasets, which consists of the following 40 different physics formulas:
+
+| ID        | Formula                                                                                     |
+|-----------|---------------------------------------------------------------------------------------------|
+| I.8.14    | \\(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\) |
+| I.10.7    | \\(m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}\\) |
+| I.11.19   | \\(A = x_1 y_1+x_2 y_2+x_3 y_3\\) |
+| I.12.2    | \\(F = \frac{q_1 q_2}{4 \pi \epsilon r^2}\\) |
+| I.12.11   | \\(F = q \left(E + B v \sin\left(\theta\right)\right)\\) |
+| I.13.4    | \\(K = \frac{1}{2} m (v^2 + u^2 + w^2)\\) |
+| I.13.12   | \\(U = G m_1 m_2 \left(\frac{1}{r_2}-\frac{1}{r_1}\right)\\) |
+| I.15.10   | \\(p = \frac{m_0 v}{\sqrt{1-v^2/c^2}}\\) |
+| I.16.6    | \\(v_1 = \frac{u+v}{1+u v/c^2}\\) |
+| I.18.4    | \\(r = \frac{m_1 r_1+m_2 r_2}{m_1+m_2}\\) |
+| I.24.6    | \\(E = \frac{1}{4} m (\omega^2+\omega_0^2) x^2\\) |
+| I.29.4    | \\(k = \frac{\omega}{c}\\) |
+| I.32.5    | \\(P = \frac{q^2 a^2}{6 \pi \epsilon c^3}\\) |
+| I.34.8    | \\(\omega = \frac{q v B}{p}\\) |
+| I.34.10   | \\(\omega = \frac{\omega_0}{1-v/c}\\) |
+| I.34.27   | \\(W = \frac{h}{2 \pi} \omega\\) |
+| I.38.12   | \\(r = 4 \pi \epsilon \frac{\left(h/\left(2 \pi\right)\right)^2}{m q^2}\\) |
+| I.39.10   | \\(U = \frac{3}{2} P V\\) |
+| I.39.11   | \\(U = \frac{P V}{\gamma-1}\\) |
+| I.43.31   | \\(D = \mu k T\\) |
+| I.43.43   | \\(\kappa = \frac{1}{\gamma - 1} \frac{k v}{\sigma_c}\\) |
+| I.48.2    | \\(E = \frac{m c^2}{\sqrt{1-v^2/c^2}}\\) |
+| II.6.11   | \\(\phi = \frac{1}{4 \pi \epsilon} \frac{p \cos\theta}{r^2}\\) |
+| II.8.7    | \\(U = \frac{3}{5}  \frac{Q^2}{4 \pi \epsilon a}\\) |
+| II.11.3   | \\(x = \frac{q E}{m (\omega_0^2-\omega^2)}\\) |
+| II.21.32  | \\(\phi = \frac{q}{4 \pi \epsilon r (1-v/c)}\\) |
+| II.34.2   | \\(\mu = \frac{q v r}{2}\\) |
+| II.34.2a  | \\(I = \frac{q v}{2 \pi r}\\) |
+| II.34.29a | \\(\mu = \frac{q h}{4 \pi m}\\) |
+| II.37.1   | \\(E = \mu (1+\chi) B\\) |
+| III.4.32  | \\(n = \frac{1}{\exp(h \omega/2 \pi k T) - 1}\\) |
+| III.8.54  | \\(|C|^2 = \sin^2 \frac{2 \pi A t}{h}\\) |
+| III.13.18 | \\(v = \frac{4 \pi A b^2}{h} k\\) |
+| III.14.14 | \\(I = I_0 \left(\exp\left(q \Delta V/\kappa T\right)-1\right)\\) |
+| III.15.12 | \\(E = 2 A (1-\cos k d)\\) |
+| III.15.14 | \\(m = \frac{h^2}{8 \pi^2 A b^2}\\) |
+| III.17.37 | \\(f = \beta (1+\alpha \cos\theta)\\) |
+| III.19.51 | \\(E = -\frac{m q^4}{2 (4 \pi \epsilon)^2 (h/(2 \pi))^2 n^2}\\) |
+| B8        | \\(U = \frac{E}{1+\frac{E}{m c^2} (1-\cos\theta)}\\) |
+| B18       | \\(\rho = \frac{3}{8 \pi G} \left(\frac{c^2 k_\text{f}}{a_\text{f}^2}+H^2\right)\\) |
 
 
 ### Supported Tasks and Leaderboards
@@ -83,7 +126,7 @@ For each dataset, we have
 1. train split (txt file, whitespace as a delimiter)
 2. val split (txt file, whitespace as a delimiter)
 3. test split (txt file, whitespace as a delimiter)
-4. true equation (pickle file)
+4. true equation (pickle file for sympy object)
 
 ### Data Splits