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Update BENCHMARKS.md
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BENCHMARKS.md

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@@ -69,6 +69,7 @@ Integrand | Approximation error | Notes
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$$\int_0^2 4x^3 - 3x^2 \mathrm{d}x$$ | 1e-14 | Trivial Integration to showcase accuracy levels |
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$$\int_0^1 (2x + yz) \mathrm{d}x$$ | 1e-30 | High accuracy for simple multivariable integrals |
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$$\int_0^1\int_0^1 (x^3 y + y^3 z) \mathrm{d}x\mathrm{d}y$$ | 1e-30 | Can handle integration by parts easily|
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$$\int_0^1\int_0^1\int_0^1 (x^3 y + y^3 z) \mathrm{d}x\mathrm{d}x\mathrm{d}y$$ | 1e-15 | High accuracy for higher order integrals|
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$$\int_{0}^1 (Sin(x) - \sqrt{x})e^{-x} \mathrm{d}x$$ | 1e-2 | Poor performance for non-polynomial integrands |
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@@ -78,6 +79,7 @@ Integrand | Approximation error | Notes
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-------------------------------------- | ------------------- | ------------------------------------------------------- |
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$$\int_{0}^\infty x^2 e^{-x} \mathrm{d}x$$ | 1e-30 | Trivial Integration to showcase accuracy levels |
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$$\int_{0}^\infty (4x^3 - 3x^2)e^{-x} \mathrm{d}x$$ | 1e-12 | High accuracy for more complicated integrands |
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$$\int_{0}^\infty\int_{0}^\infty\int_{0}^\infty (x^3 y + y^3 z)e^{-x} \mathrm{d}x\mathrm{d}x\mathrm{d}y$$ | 1e-9 | High accuracy for higher order integrals|
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$$\int_{0}^\infty (Sin(x) - \sqrt{x})e^{-x} \mathrm{d}x$$ | 1e-2 | Poor performance for non-polynomial integrands |
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Gauss-Hermite
@@ -86,5 +88,6 @@ Integrand | Approximation error | Notes
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-------------------------------------- | ------------------- | ------------------------------------------------------- |
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$$\int_{-\infty}^\infty x^2 e^{-x^2} \mathrm{d}x$$ | 1e-30 | Trivial Integration to showcase accuracy levels |
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$$\int_{-\infty}^\infty (4x^3 - 3x^2)e^{-x^2} \mathrm{d}x$$ | 1e-12 | High accuracy for more complicated integrands |
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$$\int_{0}^\infty\int_{0}^\infty\int_{0}^\infty (x^3 y + y^3 z)e^{-x^2} \mathrm{d}x\mathrm{d}x\mathrm{d}y$$ | 1e-9 | High accuracy for higher order integrals|
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$$\int_{-\infty}^\infty (Sin(x) - \sqrt{x})e^{-x^2} \mathrm{d}x$$ | 1e-1 | Poor performance for non-polynomial integrands |
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