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{"feynman-i.6.20": {"dataset_class_key": "FeynmanICh6Eq20", "sympy_eq_str": "sqrt(2)*exp(-x0**2/(2*x1**2))/(2*sqrt(pi)*x1)", "sympy_eq_srepr": "Mul(Rational(1, 2), Pow(Integer(2), Rational(1, 2)), Pow(pi, Rational(-1, 2)), Pow(Symbol('x1', real=True), Integer(-1)), exp(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('x0', real=True), Integer(2)), Pow(Symbol('x1', real=True), Integer(-2)))))", "symbols": ["$f$", "$\\theta$", "$\\sigma$"], "symbols_descs": ["Probability density function", "Position", "Standard deviation"], "si-derived_units": ["$1$", "$1$", "$1$"], "si_units": ["$1$", "$1$", "$1$"], "properties": ["V, F", "V, F", "V, F, P"]}, "feynman-i.6.20a": {"dataset_class_key": "FeynmanICh6Eq20a", "sympy_eq_str": "sqrt(2)*exp(-x0**2/2)/(2*sqrt(pi))", "sympy_eq_srepr": "Mul(Rational(1, 2), Pow(Integer(2), Rational(1, 2)), Pow(pi, Rational(-1, 2)), exp(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('x0', real=True), Integer(2)))))", "symbols": ["$f$", "$\\theta$"], "symbols_descs": ["Probability density function", "Position"], "si-derived_units": ["$1$", "$1$"], "si_units": ["$1$", "$1$"], "properties": ["V, F", "V, F"]}, "feynman-i.6.20b": {"dataset_class_key": "FeynmanICh6Eq20b", "sympy_eq_str": "sqrt(2)*exp(-(x0 - x1)**2/(2*x2**2))/(2*sqrt(pi))", "sympy_eq_srepr": "Mul(Rational(1, 2), Pow(Integer(2), Rational(1, 2)), Pow(pi, Rational(-1, 2)), exp(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('x2', real=True), Integer(-2)), Pow(Add(Symbol('x0', real=True), Mul(Integer(-1), Symbol('x1', real=True))), Integer(2)))))", "symbols": ["$f$", "$\\theta$", "$\\theta_1$", "$\\sigma$"], "symbols_descs": ["Probability density function", "Position", "Position", "Standard deviation"], "si-derived_units": ["$1$", "$1$", "$1$", "$1$"], "si_units": ["$1$", "$1$", "$1$", "$1$"], "properties": ["V, F", "V, F", "V, F", "V, F, P"]}, "feynman-i.9.18": {"dataset_class_key": "FeynmanICh9Eq18", "sympy_eq_str": "6.6743e-11*x0*x1/((x2 - x3)**2 + (x4 - x5)**2 + (x6 - x7)**2)", 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