def steep_step_verbose(f, values, x, y, h):
(xi, yi) = values
dfdx = Derivative(f,x).doit()
print('df/dx: ' + str(dfdx))
dfdx = dfdx.evalf(subs = {x:xi, y:yi})
print('df/dx @ ' + str(values) + ': ' + str(dfdx))
dfdy = Derivative(f,y).doit()
print('df/dy: ' + str(dfdy))
dfdy = dfdy.evalf(subs = {x:xi, y:yi})
print('df/dy @ ' + str(values) + ': ' + str(dfdy))
xnew = xi + dfdx*h
print('x = ' + str(xnew))
ynew = yi + dfdy*h
print('y = ' + str(ynew))
g = f.subs(x, xnew)
g = g.subs(y,ynew)
print('g(h) = ' + str(g))
dgdh = Derivative(g,h).doit()
print("g'(h) = " + str(dgdh))
H = solve(dgdh, h)
print('Solutions of h: ' + str(len(H)))
H = H[0]
print('h* = ' + str(H))
xnew = xi + dfdx*H
ynew = yi + dfdy*H
print('(x,y) = ' + str((xnew, ynew)))
return (xnew, ynew)
