Benchmarks

Several tests are available for the user to benchmark Pyccel against other common accelerators, notably pythran and numba. The same code is used for all tests, only the decorators change.

The dependencies can be installed using the command python3 -m pip install .

The code can be executed by running the script benchmarks/run_benchmarks.py.

In order to test pyccel and/or pythran, configuration files must be provided. An example configuration for pythran is found in benchmarks/config.pythranrc. This configuration is the default pythran configuration with the following additional flags:

• -O3
• -march=native
• -mtune=native
• -mavx
• -ffast-math Pyccel configurations valid for your machine can be generated using the following command (which may be adapted for c generation or other compiler languages, see the pyccel documentation):

pyccel --language=fortran --export-compile-info pyccel_fortran.json

This configuration can then be modified to include additional flags or use different compilers. The tests shown below add the following additional flags (which match the flags added to pythran):

• -O3
• -march=native
• -mtune=native
• -mavx
• -ffast-math

Additional options can be used with this script to add further comparisons, change the output format, or change what is generated.

Run python3 benchmarks/run_benchmarks.py --help for more details.

The results below are presented for the current state of the development branch of pyccel, as well as the most recent version of pyccel available on pypi.

A requirements.txt file providing the necessary packages to reproduce the tests run can be found in the version_specific_results folder. The environment can be reproduced using the following commands:

python3 -m venv my_virtual_environment
source my_virtual_environment/bin/activate
pip3 install -r requirements.txt

Tests used

The tests used can be found in the benchmarks/tests directory.

Ackermann

A basic implementation of the Ackermann function which is one of the simplest and oldest examples of a total computable function that is not primitive recursive.

Bellman Ford

An algorithm for solving the shortest path problem. The code is adapted from examples written by J. Burkardt

Djikstra

An algorithm for solving the shortest path problem. The code is adapted from examples written by J. Burkardt

Euler

Solves an ordinary differential equation using Euler's method. The code is adapted from examples written by J. Burkardt

Midpoint Explicit

Solves an ordinary differential equation using the explicit midpoint method. The code is adapted from examples written by J. Burkardt

Midpoint Fixed

Solves an ordinary differential equation using the implicit midpoint method with a fixed number of iterations. The code is adapted from examples written by J. Burkardt

RK4

Solves an ordinary differential equation using a fourth order Runge-Kutta method. The code is adapted from examples written by J. Burkardt

FD - Linear Convection

Solves a 1D linear convection problem using Finite Differences methods. The code is adapted from examples written by L. A. Barba

FD - Non-Linear Convection

Solves a 1D non-linear convection problem using Finite Differences methods. The code is adapted from examples written by L. A. Barba

FD - Poisson

Solves a 2D Poisson problem using Finite Differences methods. The code is adapted from examples written by L. A. Barba

FD - Laplace

Solves a 2D Laplace problem using Finite Differences methods. The code is adapted from examples written by L. A. Barba

MD

Runs a molecular dynamics simulation. The code is adapted from examples written by J. Burkardt

Development branch results

Performance Comparison (as of Wed Nov 27 15:03:18 UTC 2024)

Compilation time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann	-	2.28	2.10	0.33	1.33	1.33	1.49	1.48
Bellman Ford	-	3.58	3.83	1.14	3.73	4.07	3.89	4.06
Dijkstra	-	2.39	2.79	1.63	3.86	4.11	4.00	4.23
Euler	-	2.65	3.03	2.02	3.65	3.96	3.80	4.01
Midpoint Explicit	-	3.01	3.40	2.99	3.86	4.20	4.05	4.18
Midpoint Fixed	-	3.50	3.98	3.22	4.05	4.42	4.08	4.24
RK4	-	3.70	4.17	3.74	4.41	4.62	4.47	4.75
FD - L Convection	-	2.30	2.67	0.89	1.42	3.94	1.59	3.90
FD - NL Convection	-	3.27	3.51	0.88	1.40	3.93	1.61	3.90
FD - Poisson	-	3.36	3.73	1.33	1.53	4.04	2.86	4.02
FD - Laplace	-	6.53	7.97	3.03	1.84	4.37	2.11	4.26
M-D	-	6.39	6.68	4.06	-	-	-	-

Execution time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann (ms)	292.00	2.85	3.03	9.76	1.50	1.55	9.35	4.33
Bellman Ford (ms)	1760.00	5.25	3.41	3.94	2.96	6.15	-	19.30
Dijkstra (ms)	4900.00	25.60	16.10	20.40	17.90	31.60	-	22.70
Euler (ms)	3810.00	24.70	25.40	37.10	15.90	143.00	14.00	127.00
Midpoint Explicit (ms)	7800.00	52.70	51.20	78.50	23.60	280.00	16.90	250.00
Midpoint Fixed (ms)	39400.00	252.00	92.90	376.00	75.10	1380.00	58.80	1210.00
RK4 (ms)	19900.00	163.00	35.10	138.00	34.60	487.00	37.30	402.00
FD - L Convection (ms)	2210.00	1.70	1.62	2.68	1.62	1.84	-	4.07
FD - NL Convection (ms)	2690.00	1.82	1.68	2.83	1.85	2.19	-	4.29
FD - Poisson (ms)	6260.00	2.96	5.44	7.26	2.76	3.74	-	4.93
FD - Laplace (ms)	590.00	64.40	143.00	246.00	62.60	280.00	-	273.00
M-D (ms)	14700.00	15.20	52.70	59.00	-	-	-	-

Python 3.8 results

Performance Comparison (as of 1.12.1)

Compilation time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann	-	1.82	1.93	0.34	1.29	1.26	1.37	1.34
Bellman Ford	-	3.24	3.85	1.24	3.74	4.01	3.85	4.58
Dijkstra	-	2.24	2.60	1.70	3.83	4.03	3.95	4.69
Euler	-	2.47	2.92	2.04	3.63	4.00	3.87	4.56
Midpoint Explicit	-	2.82	3.46	3.08	3.85	4.17	3.98	4.65
Midpoint Fixed	-	3.30	3.92	3.38	3.99	4.38	4.03	4.77
RK4	-	3.46	4.09	3.79	4.35	4.59	4.46	5.11
FD - L Convection	-	2.07	2.60	0.92	3.56	3.84	3.69	4.38
FD - NL Convection	-	2.99	3.44	0.91	3.57	3.90	3.72	4.46
FD - Poisson	-	3.10	3.62	1.35	3.68	3.99	4.91	4.48
FD - Laplace	-	6.13	8.65	3.04	4.02	4.32	4.26	4.95
M-D	-	5.98	7.55	4.03	4.39	4.49	4.57	5.35

Execution time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann (ms)	384.00 $\pm$ 4.00	2.94 $\pm$ 0.02	3.06 $\pm$ 0.02	10.90 $\pm$ 0.10	1.56 $\pm$ 0.00	1.56 $\pm$ 0.01	9.11 $\pm$ 0.12	4.80 $\pm$ 0.01
Bellman Ford (ms)	2000.00 $\pm$ 20.00	4.54 $\pm$ 0.08	3.19 $\pm$ 0.05	3.89 $\pm$ 0.08	2.99 $\pm$ 0.02	6.19 $\pm$ 0.05	4.43 $\pm$ 0.03	18.50 $\pm$ 0.30
Dijkstra (ms)	5050.00 $\pm$ 50.00	23.80 $\pm$ 0.20	16.90 $\pm$ 0.20	20.50 $\pm$ 0.40	19.70 $\pm$ 0.30	31.10 $\pm$ 0.20	25.40 $\pm$ 0.30	23.10 $\pm$ 0.10
Euler (ms)	3990.00 $\pm$ 40.00	29.10 $\pm$ 9.50	25.80 $\pm$ 1.40	39.30 $\pm$ 1.10	15.40 $\pm$ 0.70	147.00 $\pm$ 3.00	14.30 $\pm$ 0.50	129.00 $\pm$ 1.00
Midpoint Explicit (ms)	8130.00 $\pm$ 70.00	52.70 $\pm$ 0.40	52.10 $\pm$ 1.40	82.50 $\pm$ 2.60	23.50 $\pm$ 0.50	287.00 $\pm$ 3.00	16.20 $\pm$ 0.40	256.00 $\pm$ 2.00
Midpoint Fixed (ms)	41800.00 $\pm$ 400.00	254.00 $\pm$ 1.00	92.70 $\pm$ 0.40	399.00 $\pm$ 11.00	76.70 $\pm$ 0.70	1410.00 $\pm$ 10.00	61.70 $\pm$ 1.70	1250.00 $\pm$ 20.00
RK4 (ms)	21000.00 $\pm$ 200.00	160.00 $\pm$ 4.00	36.30 $\pm$ 1.10	147.00 $\pm$ 4.00	35.40 $\pm$ 0.70	496.00 $\pm$ 8.00	39.00 $\pm$ 1.90	416.00 $\pm$ 4.00
FD - L Convection (ms)	2450.00 $\pm$ 20.00	1.55 $\pm$ 0.05	1.54 $\pm$ 0.03	2.73 $\pm$ 0.05	1.56 $\pm$ 0.06	1.85 $\pm$ 0.01	1.32 $\pm$ 0.01	4.19 $\pm$ 0.10
FD - NL Convection (ms)	3020.00 $\pm$ 30.00	1.80 $\pm$ 0.02	1.72 $\pm$ 0.01	2.82 $\pm$ 0.04	1.77 $\pm$ 0.10	2.20 $\pm$ 0.04	1.54 $\pm$ 0.03	4.20 $\pm$ 0.03
FD - Poisson (ms)	6450.00 $\pm$ 50.00	3.01 $\pm$ 0.03	5.72 $\pm$ 0.16	7.23 $\pm$ 0.03	2.81 $\pm$ 0.07	3.86 $\pm$ 0.04	2.72 $\pm$ 0.01	5.72 $\pm$ 0.02
FD - Laplace (ms)	425.00 $\pm$ 174.00	68.80 $\pm$ 0.50	151.00 $\pm$ 1.00	253.00 $\pm$ 1.00	58.70 $\pm$ 0.50	286.00 $\pm$ 1.00	64.10 $\pm$ 0.70	336.00 $\pm$ 2.00
M-D (ms)	15800.00 $\pm$ 200.00	15.30 $\pm$ 0.20	53.20 $\pm$ 0.30	59.50 $\pm$ 0.30	54.10 $\pm$ 0.20	59.90 $\pm$ 0.20	82.10 $\pm$ 6.80	61.70 $\pm$ 0.30

Python 3.9 results

Performance Comparison (as of 1.12.1)

Compilation time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann	-	1.80	1.93	0.33	1.30	1.25	1.36	1.34
Bellman Ford	-	3.24	3.55	1.11	3.63	3.93	3.74	4.45
Dijkstra	-	2.18	2.54	1.61	3.71	3.91	3.83	4.48
Euler	-	2.45	2.88	2.06	3.61	3.90	3.70	4.41
Midpoint Explicit	-	2.81	3.29	3.06	3.93	4.14	3.92	4.62
Midpoint Fixed	-	3.19	3.73	3.29	3.87	4.20	3.99	4.76
RK4	-	3.46	4.06	3.82	4.33	4.55	4.42	5.10
FD - L Convection	-	2.07	2.55	0.88	3.55	3.85	3.69	4.38
FD - NL Convection	-	2.96	3.44	0.89	3.57	3.86	3.72	4.38
FD - Poisson	-	3.07	3.63	1.36	3.69	4.00	4.94	4.50
FD - Laplace	-	6.17	8.76	3.07	4.02	4.32	4.25	4.88
M-D	-	6.02	7.59	4.09	4.37	4.49	4.53	5.35

Execution time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann (ms)	333.00 $\pm$ 3.00	2.97 $\pm$ 0.03	3.06 $\pm$ 0.01	10.80 $\pm$ 0.20	1.51 $\pm$ 0.00	1.56 $\pm$ 0.00	7.51 $\pm$ 0.20	4.36 $\pm$ 0.00
Bellman Ford (ms)	1920.00 $\pm$ 20.00	4.60 $\pm$ 0.02	3.19 $\pm$ 0.05	3.91 $\pm$ 0.06	3.01 $\pm$ 0.02	6.08 $\pm$ 0.03	4.33 $\pm$ 0.06	18.50 $\pm$ 0.40
Dijkstra (ms)	5150.00 $\pm$ 60.00	24.90 $\pm$ 0.10	16.40 $\pm$ 0.10	19.70 $\pm$ 0.20	18.10 $\pm$ 0.30	30.00 $\pm$ 0.30	24.10 $\pm$ 0.20	22.40 $\pm$ 0.20
Euler (ms)	3880.00 $\pm$ 30.00	25.70 $\pm$ 0.40	26.60 $\pm$ 3.60	37.50 $\pm$ 0.40	15.00 $\pm$ 0.50	144.00 $\pm$ 2.00	13.80 $\pm$ 0.30	128.00 $\pm$ 2.00
Midpoint Explicit (ms)	7930.00 $\pm$ 90.00	53.10 $\pm$ 0.70	52.00 $\pm$ 0.90	76.50 $\pm$ 0.50	23.50 $\pm$ 0.40	284.00 $\pm$ 2.00	16.00 $\pm$ 0.40	256.00 $\pm$ 5.00
Midpoint Fixed (ms)	40300.00 $\pm$ 300.00	253.00 $\pm$ 1.00	92.80 $\pm$ 0.50	368.00 $\pm$ 2.00	75.70 $\pm$ 0.60	1420.00 $\pm$ 20.00	74.40 $\pm$ 38.60	1240.00 $\pm$ 10.00
RK4 (ms)	20200.00 $\pm$ 100.00	160.00 $\pm$ 4.00	36.00 $\pm$ 0.80	137.00 $\pm$ 1.00	35.30 $\pm$ 0.60	495.00 $\pm$ 13.00	37.20 $\pm$ 0.50	414.00 $\pm$ 7.00
FD - L Convection (ms)	2360.00 $\pm$ 10.00	1.66 $\pm$ 0.03	1.56 $\pm$ 0.02	2.74 $\pm$ 0.07	1.76 $\pm$ 0.03	1.75 $\pm$ 0.11	1.54 $\pm$ 0.01	4.18 $\pm$ 0.10
FD - NL Convection (ms)	2940.00 $\pm$ 20.00	1.58 $\pm$ 0.02	1.74 $\pm$ 0.04	2.83 $\pm$ 0.03	2.07 $\pm$ 0.19	2.02 $\pm$ 0.06	1.53 $\pm$ 0.01	4.19 $\pm$ 0.03
FD - Poisson (ms)	6610.00 $\pm$ 120.00	3.18 $\pm$ 0.02	5.83 $\pm$ 0.13	7.25 $\pm$ 0.06	2.83 $\pm$ 0.03	3.87 $\pm$ 0.04	2.70 $\pm$ 0.02	5.71 $\pm$ 0.02
FD - Laplace (ms)	600.00 $\pm$ 14.00	69.00 $\pm$ 0.40	151.00 $\pm$ 1.00	253.00 $\pm$ 1.00	63.30 $\pm$ 0.60	260.00 $\pm$ 1.00	64.20 $\pm$ 0.50	322.00 $\pm$ 1.00
M-D (ms)	15600.00 $\pm$ 100.00	15.30 $\pm$ 0.10	53.10 $\pm$ 0.20	59.60 $\pm$ 0.30	54.50 $\pm$ 0.20	59.50 $\pm$ 0.20	80.00 $\pm$ 0.50	60.50 $\pm$ 0.20

Python 3.10 results

Performance Comparison (as of 1.12.1)

Compilation time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann	-	2.19	2.09	0.33	1.26	1.21	1.32	1.30
Bellman Ford	-	3.31	3.65	1.10	3.60	3.85	3.67	4.38
Dijkstra	-	2.30	2.68	1.62	3.64	3.88	3.81	4.43
Euler	-	2.57	3.03	2.06	3.55	3.87	3.66	4.36
Midpoint Explicit	-	2.91	3.45	3.07	3.79	4.15	3.88	4.55
Midpoint Fixed	-	3.28	3.86	3.29	3.84	4.16	3.94	4.64
RK4	-	3.58	4.18	3.85	4.27	4.55	4.34	5.04
FD - L Convection	-	2.22	2.69	0.89	3.51	3.82	3.58	4.32
FD - NL Convection	-	3.12	3.59	0.91	3.57	3.84	3.68	4.32
FD - Poisson	-	3.21	3.75	1.36	3.65	3.94	4.87	4.44
FD - Laplace	-	6.29	8.89	3.10	3.99	4.25	4.20	4.85
M-D	-	6.14	7.72	4.12	4.31	4.41	4.46	5.29

Execution time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann (ms)	302.00 $\pm$ 2.00	2.90 $\pm$ 0.04	3.08 $\pm$ 0.07	10.70 $\pm$ 0.30	1.56 $\pm$ 0.00	1.57 $\pm$ 0.04	9.47 $\pm$ 0.24	3.95 $\pm$ 0.00
Bellman Ford (ms)	1810.00 $\pm$ 60.00	5.27 $\pm$ 0.03	3.19 $\pm$ 0.05	3.86 $\pm$ 0.06	3.00 $\pm$ 0.02	6.02 $\pm$ 0.02	4.43 $\pm$ 0.01	18.70 $\pm$ 0.30
Dijkstra (ms)	4920.00 $\pm$ 40.00	24.70 $\pm$ 0.20	16.60 $\pm$ 1.50	19.10 $\pm$ 0.30	18.20 $\pm$ 0.20	30.40 $\pm$ 0.20	23.20 $\pm$ 0.20	22.00 $\pm$ 0.20
Euler (ms)	3890.00 $\pm$ 60.00	25.40 $\pm$ 0.40	25.50 $\pm$ 1.00	37.80 $\pm$ 0.40	15.30 $\pm$ 0.40	148.00 $\pm$ 9.00	13.70 $\pm$ 0.30	129.00 $\pm$ 3.00
Midpoint Explicit (ms)	7860.00 $\pm$ 70.00	54.70 $\pm$ 4.10	51.70 $\pm$ 0.60	80.40 $\pm$ 6.10	23.70 $\pm$ 1.60	284.00 $\pm$ 3.00	16.20 $\pm$ 0.80	255.00 $\pm$ 2.00
Midpoint Fixed (ms)	40000.00 $\pm$ 200.00	254.00 $\pm$ 1.00	92.40 $\pm$ 0.30	383.00 $\pm$ 4.00	75.60 $\pm$ 0.90	1410.00 $\pm$ 20.00	60.70 $\pm$ 1.30	1250.00 $\pm$ 10.00
RK4 (ms)	20100.00 $\pm$ 200.00	160.00 $\pm$ 2.00	35.80 $\pm$ 0.90	139.00 $\pm$ 2.00	35.20 $\pm$ 0.60	495.00 $\pm$ 4.00	37.20 $\pm$ 0.50	412.00 $\pm$ 4.00
FD - L Convection (ms)	2240.00 $\pm$ 20.00	1.65 $\pm$ 0.03	1.56 $\pm$ 0.03	2.77 $\pm$ 0.07	1.68 $\pm$ 0.06	1.87 $\pm$ 0.03	1.33 $\pm$ 0.01	4.15 $\pm$ 0.05
FD - NL Convection (ms)	2740.00 $\pm$ 10.00	1.79 $\pm$ 0.03	1.73 $\pm$ 0.06	2.94 $\pm$ 0.12	2.03 $\pm$ 0.19	2.18 $\pm$ 0.03	1.54 $\pm$ 0.04	4.15 $\pm$ 0.06
FD - Poisson (ms)	6410.00 $\pm$ 90.00	2.99 $\pm$ 0.04	5.67 $\pm$ 0.04	7.35 $\pm$ 0.24	2.83 $\pm$ 0.04	3.86 $\pm$ 0.02	2.71 $\pm$ 0.02	5.73 $\pm$ 0.02
FD - Laplace (ms)	608.00 $\pm$ 15.00	67.50 $\pm$ 1.70	151.00 $\pm$ 2.00	247.00 $\pm$ 1.00	60.50 $\pm$ 2.10	310.00 $\pm$ 2.00	63.90 $\pm$ 0.60	327.00 $\pm$ 1.00
M-D (ms)	15100.00 $\pm$ 100.00	15.30 $\pm$ 0.00	53.00 $\pm$ 0.20	59.50 $\pm$ 0.30	54.00 $\pm$ 0.10	59.90 $\pm$ 0.30	81.10 $\pm$ 0.10	62.30 $\pm$ 2.00

Python 3.11 results

Performance Comparison (as of 1.12.1)

Compilation time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann	-	2.20	2.12	0.29	1.36	1.27	1.42	1.39
Bellman Ford	-	3.35	3.67	1.13	3.69	3.87	3.83	4.48
Dijkstra	-	2.18	2.55	1.55	3.60	3.82	3.77	4.36
Euler	-	2.44	2.90	1.95	3.49	3.81	3.60	4.28
Midpoint Explicit	-	2.78	3.26	2.90	3.73	4.05	3.86	4.50
Midpoint Fixed	-	3.12	3.69	3.11	3.78	4.10	3.90	4.58
RK4	-	3.40	4.01	3.61	4.18	4.44	4.25	4.96
FD - L Convection	-	2.15	2.62	0.84	3.48	3.78	3.62	4.29
FD - NL Convection	-	3.02	3.50	0.83	3.48	3.81	3.66	4.29
FD - Poisson	-	3.07	3.56	1.27	3.61	3.91	4.82	4.40
FD - Laplace	-	6.10	8.65	2.87	3.90	4.20	4.15	4.75
M-D	-	6.13	7.47	3.98	4.22	4.36	4.38	5.21

Execution time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann (ms)	434.00 $\pm$ 8.00	2.90 $\pm$ 0.05	3.06 $\pm$ 0.00	10.70 $\pm$ 0.30	1.56 $\pm$ 0.01	1.56 $\pm$ 0.01	9.89 $\pm$ 0.57	4.39 $\pm$ 0.09
Bellman Ford (ms)	1890.00 $\pm$ 10.00	5.27 $\pm$ 0.03	3.18 $\pm$ 0.06	3.89 $\pm$ 0.16	3.01 $\pm$ 0.02	6.10 $\pm$ 0.03	4.06 $\pm$ 0.04	18.70 $\pm$ 0.40
Dijkstra (ms)	4870.00 $\pm$ 80.00	23.50 $\pm$ 0.40	15.90 $\pm$ 0.10	18.90 $\pm$ 0.30	17.70 $\pm$ 0.60	30.10 $\pm$ 0.20	23.40 $\pm$ 0.30	21.70 $\pm$ 0.10
Euler (ms)	3850.00 $\pm$ 30.00	25.40 $\pm$ 0.50	25.40 $\pm$ 1.00	37.30 $\pm$ 0.30	15.30 $\pm$ 0.70	144.00 $\pm$ 2.00	13.70 $\pm$ 0.40	128.00 $\pm$ 2.00
Midpoint Explicit (ms)	7930.00 $\pm$ 130.00	52.60 $\pm$ 0.30	52.90 $\pm$ 2.20	76.90 $\pm$ 1.40	23.00 $\pm$ 0.50	285.00 $\pm$ 2.00	15.90 $\pm$ 0.40	253.00 $\pm$ 3.00
Midpoint Fixed (ms)	40200.00 $\pm$ 400.00	257.00 $\pm$ 5.00	92.60 $\pm$ 1.10	367.00 $\pm$ 2.00	75.10 $\pm$ 0.50	1410.00 $\pm$ 20.00	61.40 $\pm$ 2.00	1240.00 $\pm$ 20.00
RK4 (ms)	19800.00 $\pm$ 100.00	162.00 $\pm$ 2.00	35.50 $\pm$ 0.60	137.00 $\pm$ 1.00	32.60 $\pm$ 1.00	499.00 $\pm$ 14.00	37.80 $\pm$ 0.60	415.00 $\pm$ 17.00
FD - L Convection (ms)	2220.00 $\pm$ 20.00	1.66 $\pm$ 0.05	1.56 $\pm$ 0.04	2.73 $\pm$ 0.06	1.50 $\pm$ 0.05	1.74 $\pm$ 0.12	1.54 $\pm$ 0.04	4.19 $\pm$ 0.03
FD - NL Convection (ms)	2750.00 $\pm$ 20.00	1.82 $\pm$ 0.18	1.70 $\pm$ 0.07	2.84 $\pm$ 0.05	1.97 $\pm$ 0.29	2.08 $\pm$ 0.12	1.53 $\pm$ 0.01	4.20 $\pm$ 0.03
FD - Poisson (ms)	6190.00 $\pm$ 110.00	3.06 $\pm$ 0.22	5.65 $\pm$ 0.03	7.23 $\pm$ 0.06	2.79 $\pm$ 0.02	3.83 $\pm$ 0.02	2.67 $\pm$ 0.02	5.70 $\pm$ 0.02
FD - Laplace (ms)	594.00 $\pm$ 3.00	68.00 $\pm$ 0.70	150.00 $\pm$ 1.00	246.00 $\pm$ 1.00	60.10 $\pm$ 2.10	257.00 $\pm$ 2.00	63.50 $\pm$ 0.50	327.00 $\pm$ 1.00
M-D (ms)	14900.00 $\pm$ 200.00	15.30 $\pm$ 0.10	53.20 $\pm$ 0.20	59.60 $\pm$ 0.30	54.80 $\pm$ 0.20	59.60 $\pm$ 0.20	80.30 $\pm$ 0.20	61.30 $\pm$ 0.20

Python 3.12 results

Performance Comparison (as of 1.12.1)

Compilation time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann	-	1.95	-	0.30	1.39	1.32	1.42	1.40
Bellman Ford	-	3.33	-	1.21	3.78	3.97	3.83	4.45
Dijkstra	-	2.41	-	1.74	3.86	3.99	3.92	4.55
Euler	-	2.54	-	2.03	3.63	3.94	3.80	4.43
Midpoint Explicit	-	3.01	-	3.15	4.15	4.44	4.24	4.84
Midpoint Fixed	-	3.38	-	3.28	4.02	4.47	4.13	4.85
RK4	-	3.76	-	3.85	4.59	5.13	4.85	5.52
FD - L Convection	-	2.44	-	0.95	3.83	4.08	3.89	4.64
FD - NL Convection	-	3.22	-	0.88	3.75	3.97	3.81	4.44
FD - Poisson	-	3.35	-	1.37	3.81	4.16	5.15	4.70
FD - Laplace	-	6.38	-	3.19	4.23	4.44	4.40	5.01
M-D	-	6.47	-	4.09	4.62	4.61	4.78	5.46

Execution time

Algorithm	python	pythran_gnu	pythran_intel	numba	pyccel_fortran_gnu	pyccel_c_gnu	pyccel_fortran_intel	pyccel_c_intel
Ackermann (ms)	437.00 $\pm$ 8.00	2.95 $\pm$ 0.02	-	10.80 $\pm$ 0.30	1.56 $\pm$ 0.01	1.61 $\pm$ 0.01	10.60 $\pm$ 0.20	4.37 $\pm$ 0.01
Bellman Ford (ms)	2530.00 $\pm$ 40.00	4.59 $\pm$ 0.01	-	3.87 $\pm$ 0.07	3.01 $\pm$ 0.02	5.62 $\pm$ 0.02	4.25 $\pm$ 0.05	18.60 $\pm$ 0.30
Dijkstra (ms)	6850.00 $\pm$ 40.00	26.80 $\pm$ 0.20	-	20.90 $\pm$ 0.50	19.10 $\pm$ 0.70	29.40 $\pm$ 0.10	23.00 $\pm$ 0.20	22.30 $\pm$ 0.40
Euler (ms)	4900.00 $\pm$ 40.00	25.40 $\pm$ 0.30	-	37.80 $\pm$ 0.50	15.50 $\pm$ 0.70	144.00 $\pm$ 2.00	13.80 $\pm$ 0.40	128.00 $\pm$ 1.00
Midpoint Explicit (ms)	9820.00 $\pm$ 50.00	52.60 $\pm$ 0.40	-	78.10 $\pm$ 0.60	24.40 $\pm$ 1.00	285.00 $\pm$ 4.00	16.60 $\pm$ 0.60	256.00 $\pm$ 3.00
Midpoint Fixed (ms)	48700.00 $\pm$ 400.00	254.00 $\pm$ 1.00	-	387.00 $\pm$ 2.00	75.40 $\pm$ 0.70	1410.00 $\pm$ 20.00	62.60 $\pm$ 3.30	1260.00 $\pm$ 30.00
RK4 (ms)	24500.00 $\pm$ 100.00	165.00 $\pm$ 17.00	-	147.00 $\pm$ 15.00	36.40 $\pm$ 0.60	498.00 $\pm$ 11.00	38.90 $\pm$ 0.30	417.00 $\pm$ 14.00
FD - L Convection (ms)	2950.00 $\pm$ 30.00	1.63 $\pm$ 0.01	-	2.73 $\pm$ 0.03	1.69 $\pm$ 0.01	1.75 $\pm$ 0.13	1.53 $\pm$ 0.01	4.21 $\pm$ 0.03
FD - NL Convection (ms)	3640.00 $\pm$ 40.00	1.81 $\pm$ 0.04	-	2.83 $\pm$ 0.03	1.94 $\pm$ 0.23	1.97 $\pm$ 0.01	1.40 $\pm$ 0.01	4.24 $\pm$ 0.09
FD - Poisson (ms)	8120.00 $\pm$ 110.00	2.97 $\pm$ 0.04	-	7.25 $\pm$ 0.05	2.83 $\pm$ 0.03	3.82 $\pm$ 0.04	2.68 $\pm$ 0.01	5.75 $\pm$ 0.14
FD - Laplace (ms)	602.00 $\pm$ 11.00	69.60 $\pm$ 1.70	-	248.00 $\pm$ 1.00	62.60 $\pm$ 3.70	257.00 $\pm$ 2.00	64.20 $\pm$ 1.60	329.00 $\pm$ 1.00
M-D (ms)	18900.00 $\pm$ 100.00	15.20 $\pm$ 0.00	-	60.30 $\pm$ 2.30	55.20 $\pm$ 1.90	59.80 $\pm$ 0.70	81.30 $\pm$ 0.30	61.90 $\pm$ 0.50