Artifact version: 1
Metrics¶
| Metric identity | Symbol | Value | Units | Status |
|---|---|---|---|---|
| flat_slope.bisection.executed_iterations | N_iter | 48 | iterations | info |
| flat_slope.bisection.final_absolute_residual | abs(f(x_star)) | 5.605193857299268e-45 | function units | info |
| flat_slope.bisection.final_relative_residual | R_root | 7.006492321624085e-46 | dimensionless | info |
| flat_slope.bisection.function_evaluations | N_eval | 50 | evaluations | info |
| flat_slope.bisection.warm_wall | t_wall,warm | 5.375128239393234e-06 | s | info |
| flat_slope.safeguarded_hybrid.executed_iterations | N_iter | 3 | iterations | info |
| flat_slope.safeguarded_hybrid.final_absolute_residual | abs(f(x_star)) | 0.0 | function units | info |
| flat_slope.safeguarded_hybrid.final_relative_residual | R_root | 0.0 | dimensionless | info |
| flat_slope.safeguarded_hybrid.function_evaluations | N_eval | 5 | evaluations | info |
| flat_slope.safeguarded_hybrid.warm_wall | t_wall,warm | 0.00026350002735853195 | s | info |
| linear.bisection.executed_iterations | N_iter | 48 | iterations | info |
| linear.bisection.final_absolute_residual | abs(f(x_star)) | 7.105427357601002e-15 | function units | info |
| linear.bisection.final_relative_residual | R_root | 3.552713678800501e-15 | dimensionless | info |
| linear.bisection.function_evaluations | N_eval | 50 | evaluations | info |
| linear.bisection.warm_wall | t_wall,warm | 5.332985892891884e-06 | s | info |
| linear.safeguarded_hybrid.executed_iterations | N_iter | 1 | iterations | info |
| linear.safeguarded_hybrid.final_absolute_residual | abs(f(x_star)) | 0.0 | function units | info |
| linear.safeguarded_hybrid.final_relative_residual | R_root | 0.0 | dimensionless | info |
| linear.safeguarded_hybrid.function_evaluations | N_eval | 3 | evaluations | info |
| linear.safeguarded_hybrid.warm_wall | t_wall,warm | 0.0005117498803883791 | s | info |
| monotone_kink.bisection.executed_iterations | N_iter | 48 | iterations | info |
| monotone_kink.bisection.final_absolute_residual | abs(f(x_star)) | 2.1094237467877974e-15 | function units | info |
| monotone_kink.bisection.final_relative_residual | R_root | 3.515706244646329e-15 | dimensionless | info |
| monotone_kink.bisection.function_evaluations | N_eval | 50 | evaluations | info |
| monotone_kink.bisection.warm_wall | t_wall,warm | 5.292007699608803e-06 | s | info |
| monotone_kink.safeguarded_hybrid.executed_iterations | N_iter | 48 | iterations | info |
| monotone_kink.safeguarded_hybrid.final_absolute_residual | abs(f(x_star)) | 1.6062151608764452e-13 | function units | info |
| monotone_kink.safeguarded_hybrid.final_relative_residual | R_root | 2.6770252681274087e-13 | dimensionless | info |
| monotone_kink.safeguarded_hybrid.function_evaluations | N_eval | 50 | evaluations | info |
| monotone_kink.safeguarded_hybrid.warm_wall | t_wall,warm | 0.0005734579171985388 | s | info |
| oscillatory_fixed_point_residual.bisection.executed_iterations | N_iter | 48 | iterations | info |
| oscillatory_fixed_point_residual.bisection.final_absolute_residual | abs(f(x_star)) | 6.661338147750939e-16 | function units | info |
| oscillatory_fixed_point_residual.bisection.final_relative_residual | R_root | 5.124106267500722e-16 | dimensionless | info |
| oscillatory_fixed_point_residual.bisection.function_evaluations | N_eval | 50 | evaluations | info |
| oscillatory_fixed_point_residual.bisection.warm_wall | t_wall,warm | 5.208887159824371e-06 | s | info |
| oscillatory_fixed_point_residual.safeguarded_hybrid.executed_iterations | N_iter | 1 | iterations | info |
| oscillatory_fixed_point_residual.safeguarded_hybrid.final_absolute_residual | abs(f(x_star)) | 0.0 | function units | info |
| oscillatory_fixed_point_residual.safeguarded_hybrid.final_relative_residual | R_root | 0.0 | dimensionless | info |
| oscillatory_fixed_point_residual.safeguarded_hybrid.function_evaluations | N_eval | 3 | evaluations | info |
| oscillatory_fixed_point_residual.safeguarded_hybrid.warm_wall | t_wall,warm | 0.00038466695696115494 | s | info |
| quadratic.bisection.executed_iterations | N_iter | 48 | iterations | info |
| quadratic.bisection.final_absolute_residual | abs(f(x_star)) | 2.220446049250313e-15 | function units | info |
| quadratic.bisection.final_relative_residual | R_root | 1.1102230246251565e-15 | dimensionless | info |
| quadratic.bisection.function_evaluations | N_eval | 50 | evaluations | info |
| quadratic.bisection.warm_wall | t_wall,warm | 5.249865353107452e-06 | s | info |
| quadratic.safeguarded_hybrid.executed_iterations | N_iter | 40 | iterations | info |
| quadratic.safeguarded_hybrid.final_absolute_residual | abs(f(x_star)) | 1.6106786041140528e-15 | function units | info |
| quadratic.safeguarded_hybrid.final_relative_residual | R_root | 8.053393020570264e-16 | dimensionless | info |
| quadratic.safeguarded_hybrid.function_evaluations | N_eval | 42 | evaluations | info |
| quadratic.safeguarded_hybrid.warm_wall | t_wall,warm | 0.000321083003655076 | s | info |
Comparisons¶
| Comparison | Metric | Relation | Reference | Units | Absolute tolerance | Relative tolerance | Status | Note |
|---|---|---|---|---|---|---|---|---|
| flat_slope.hybrid-no-more-evaluations | flat_slope.safeguarded_hybrid.function_evaluations | less_equal | 50 | evaluations | 0.0 | 0.0 | pass | Hybrid evaluation count must not exceed fixed-step bisection. |
| linear.hybrid-no-more-evaluations | linear.safeguarded_hybrid.function_evaluations | less_equal | 50 | evaluations | 0.0 | 0.0 | pass | Hybrid evaluation count must not exceed fixed-step bisection. |
| monotone_kink.hybrid-no-more-evaluations | monotone_kink.safeguarded_hybrid.function_evaluations | less_equal | 50 | evaluations | 0.0 | 0.0 | pass | Hybrid evaluation count must not exceed fixed-step bisection. |
| oscillatory_fixed_point_residual.hybrid-no-more-evaluations | oscillatory_fixed_point_residual.safeguarded_hybrid.function_evaluations | less_equal | 50 | evaluations | 0.0 | 0.0 | pass | Hybrid evaluation count must not exceed fixed-step bisection. |
| quadratic.hybrid-no-more-evaluations | quadratic.safeguarded_hybrid.function_evaluations | less_equal | 50 | evaluations | 0.0 | 0.0 | pass | Hybrid evaluation count must not exceed fixed-step bisection. |
Environment policy¶
Recorded execution environment; wall metrics are informational.
Limitations¶
Warm wall time is hardware- and load-dependent.
Method payload¶
{
"cases": [
{
"bracket": [
0.0,
4.0
],
"methods": {
"bisection": {
"converged": null,
"executed_iterations": {
"unit": "iterations",
"value": 48
},
"final_absolute_residual": {
"unit": "function units",
"value": 7.105427357601002e-15
},
"final_relative_residual": {
"unit": "dimensionless",
"value": 3.552713678800501e-15
},
"function_evaluations": {
"unit": "evaluations",
"value": 50
},
"status": "fixed_steps",
"warm_wall": {
"unit": "s",
"value": 5.332985892891884e-06
}
},
"safeguarded_hybrid": {
"converged": true,
"executed_iterations": {
"unit": "iterations",
"value": 1
},
"final_absolute_residual": {
"unit": "function units",
"value": 0.0
},
"final_relative_residual": {
"unit": "dimensionless",
"value": 0.0
},
"function_evaluations": {
"unit": "evaluations",
"value": 3
},
"status": 3,
"warm_wall": {
"unit": "s",
"value": 0.0005117498803883791
}
}
},
"name": "linear"
},
{
"bracket": [
0.0,
2.0
],
"methods": {
"bisection": {
"converged": null,
"executed_iterations": {
"unit": "iterations",
"value": 48
},
"final_absolute_residual": {
"unit": "function units",
"value": 2.220446049250313e-15
},
"final_relative_residual": {
"unit": "dimensionless",
"value": 1.1102230246251565e-15
},
"function_evaluations": {
"unit": "evaluations",
"value": 50
},
"status": "fixed_steps",
"warm_wall": {
"unit": "s",
"value": 5.249865353107452e-06
}
},
"safeguarded_hybrid": {
"converged": true,
"executed_iterations": {
"unit": "iterations",
"value": 40
},
"final_absolute_residual": {
"unit": "function units",
"value": 1.6106786041140528e-15
},
"final_relative_residual": {
"unit": "dimensionless",
"value": 8.053393020570264e-16
},
"function_evaluations": {
"unit": "evaluations",
"value": 42
},
"status": 4,
"warm_wall": {
"unit": "s",
"value": 0.000321083003655076
}
}
},
"name": "quadratic"
},
{
"bracket": [
0.0,
3.0
],
"methods": {
"bisection": {
"converged": null,
"executed_iterations": {
"unit": "iterations",
"value": 48
},
"final_absolute_residual": {
"unit": "function units",
"value": 5.605193857299268e-45
},
"final_relative_residual": {
"unit": "dimensionless",
"value": 7.006492321624085e-46
},
"function_evaluations": {
"unit": "evaluations",
"value": 50
},
"status": "fixed_steps",
"warm_wall": {
"unit": "s",
"value": 5.375128239393234e-06
}
},
"safeguarded_hybrid": {
"converged": true,
"executed_iterations": {
"unit": "iterations",
"value": 3
},
"final_absolute_residual": {
"unit": "function units",
"value": 0.0
},
"final_relative_residual": {
"unit": "dimensionless",
"value": 0.0
},
"function_evaluations": {
"unit": "evaluations",
"value": 5
},
"status": 3,
"warm_wall": {
"unit": "s",
"value": 0.00026350002735853195
}
}
},
"name": "flat_slope"
},
{
"bracket": [
0.0,
1.0
],
"methods": {
"bisection": {
"converged": null,
"executed_iterations": {
"unit": "iterations",
"value": 48
},
"final_absolute_residual": {
"unit": "function units",
"value": 2.1094237467877974e-15
},
"final_relative_residual": {
"unit": "dimensionless",
"value": 3.515706244646329e-15
},
"function_evaluations": {
"unit": "evaluations",
"value": 50
},
"status": "fixed_steps",
"warm_wall": {
"unit": "s",
"value": 5.292007699608803e-06
}
},
"safeguarded_hybrid": {
"converged": true,
"executed_iterations": {
"unit": "iterations",
"value": 48
},
"final_absolute_residual": {
"unit": "function units",
"value": 1.6062151608764452e-13
},
"final_relative_residual": {
"unit": "dimensionless",
"value": 2.6770252681274087e-13
},
"function_evaluations": {
"unit": "evaluations",
"value": 50
},
"status": 4,
"warm_wall": {
"unit": "s",
"value": 0.0005734579171985388
}
}
},
"name": "monotone_kink"
},
{
"bracket": [
0.0,
1.0
],
"methods": {
"bisection": {
"converged": null,
"executed_iterations": {
"unit": "iterations",
"value": 48
},
"final_absolute_residual": {
"unit": "function units",
"value": 6.661338147750939e-16
},
"final_relative_residual": {
"unit": "dimensionless",
"value": 5.124106267500722e-16
},
"function_evaluations": {
"unit": "evaluations",
"value": 50
},
"status": "fixed_steps",
"warm_wall": {
"unit": "s",
"value": 5.208887159824371e-06
}
},
"safeguarded_hybrid": {
"converged": true,
"executed_iterations": {
"unit": "iterations",
"value": 1
},
"final_absolute_residual": {
"unit": "function units",
"value": 0.0
},
"final_relative_residual": {
"unit": "dimensionless",
"value": 0.0
},
"function_evaluations": {
"unit": "evaluations",
"value": 3
},
"status": 3,
"warm_wall": {
"unit": "s",
"value": 0.00038466695696115494
}
}
},
"name": "oscillatory_fixed_point_residual"
}
],
"controls": {
"atol": 1e-12,
"bisection_steps": 48,
"hybrid_max_steps": 96,
"matched_coordinate_tolerance": {
"unit": "coordinate units",
"value": 5e-12
},
"rtol": 1e-12,
"safeguard_fraction": 0.1
},
"environment": {
"device": "cpu:0",
"git_revision": "a3f0d4bd563555e67a3ec0ca8e1ed0e8be671f60",
"jax_backend": "cpu",
"jax_version": "0.10.1",
"measured_at_utc": "2026-07-13T03:01:33.095776+00:00",
"platform": "macOS-26.1-arm64-arm-64bit-Mach-O",
"python_version": "3.13.7",
"working_tree_dirty": true
},
"precision": "float64",
"relative_residual_definition": "abs(f(root)) / max(abs(f(lo)), abs(f(hi)))",
"schema_version": 1,
"warm_repeats": 21
}