property-testing-solver-test.js

describe('newton\'s method', () => {
  it('solves polynomial functions from a guess within 0.5', () => {
    const solverTest = (polynomial, x) => {
      if (polynomial.degree <= 0) {
        return true; // no fun solving constant functions
      };

      // polynomial(x) = y, so we make a new polynomial
      // polynomialWithZero such that polynomialWithZero(x) = 0
      const y = polynomial.evaluate(x);
      const polynomialWithZero = polynomial.setCoefficient(0, polynomial.coefficients[0] - y);

      // use a random guess within 0.5 of the right answer
      const delta = jsc.random.number(-0.5, 0.5);
      const solution = newton.solve(polynomialWithZero, x + delta);

      // because we're doing analytical math with native JavaScript numbers
      // we expect floating point error, so we test
      // approximate equality w/ a custom function
      return approxEqual(polynomial.evaluate(solution), y);
    };

    const solvesPolynomialFunctions = jsc.forall(
      arbitraryPolnomial,
      jsc.integer(10),
      solverTest
    );

    // size: 10 limits the _degree_ of the polynomials tested
    // this is where we'd provide a larger size for the smap arbitrary
    jsc.assert(solvesPolynomialFunctions, { size: 10 });
  });
});