==========================================================================================
SUNBURST FAILURE MODE BENCHMARK RESULTS
==========================================================================================
Timestamp: 20260125_212644
Configuration: n_oscillations=3, greendragon_fast=False
Dimensions tested: [2, 4, 8, 16, 24, 32, 48, 64]

Function                             Dim  True log(Z)     Computed      Error Status    
------------------------------------------------------------------------------------------
student_t_nu3.0_2D                     2       1.8379       1.5379     0.3000 OK        
student_t_cauchy_2D                    2       1.8379       1.1221     0.7158 OK        
banana_b0.1_2D                         2       1.8379       1.8324     0.0055 OK        
banana_b0.5_2D                         2       1.8379       1.7457     0.0922 OK        
funnel_sigma3.0_2D                     2       0.0000      -1.1250     1.1250 DEGRADED  
exp_power_beta1.0_2D                   2       1.3863       1.2598     0.1265 OK        
exp_power_beta0.5_2D                   2       2.7726       0.9867     1.7859 DEGRADED  
ring_R3.0_w0.3_2D                      2       2.6515      16.4258    13.7743 DEGRADED  
twisted_t1.0_2D                        2       0.0000       0.3824     0.3824 OK        
skew_normal_a5.0_2D                    2       0.0000         FAIL          - FAILED    
bimodal_w0.9_2D                        2       0.0000       0.0002     0.0002 OK        
student_t_nu3.0_4D                     4       3.1649       3.1327     0.0322 OK        
student_t_cauchy_4D                    4       2.5771       1.1185     1.4586 DEGRADED  
banana_b0.1_4D                         4       3.6758       3.6715     0.0043 OK        
banana_b0.5_4D                         4       3.6758       3.5836     0.0922 OK        
funnel_sigma3.0_4D                     4       0.0000          nan        N/A DEGRADED  
exp_power_beta1.0_4D                   4       2.7726       2.8101     0.0375 OK        
exp_power_beta0.5_4D                   4       5.5452       1.9734     3.5718 DEGRADED  
ring_R3.0_w0.3_4D                      4       5.9934      37.0023    31.0089 DEGRADED  
twisted_t1.0_4D                        4       0.0000       0.3821     0.3821 OK        
skew_normal_a5.0_4D                    4       0.0000         FAIL          - FAILED    
bimodal_w0.9_4D                        4       0.0000       0.0002     0.0002 OK        
student_t_nu3.0_8D                     8       4.8948       4.8948     0.0000 OK        
student_t_cauchy_8D                    8       2.6975      -0.1604     2.8579 DEGRADED  
banana_b0.1_8D                         8       7.3515       7.3467     0.0048 OK        
banana_b0.5_8D                         8       7.3515       7.2593     0.0922 OK        
funnel_sigma3.0_8D                     8       0.0000          nan        N/A DEGRADED  
exp_power_beta1.0_8D                   8       5.5452       5.7445     0.1994 OK        
exp_power_beta0.5_8D                   8      11.0904       3.9468     7.1436 DEGRADED  
ring_R3.0_w0.3_8D                      8      10.8856      80.6318    69.7462 DEGRADED  
twisted_t1.0_8D                        8       0.0000       0.3821     0.3821 OK        
skew_normal_a5.0_8D                    8       0.0000         FAIL          - FAILED    
bimodal_w0.9_8D                        8       0.0000       0.0002     0.0002 OK        
student_t_nu3.0_16D                   16       6.1366       6.1383     0.0017 OK        
student_t_cauchy_16D                  16       0.1809       0.1540     0.0269 OK        
banana_b0.1_16D                       16      14.7030      14.6989     0.0041 OK        
funnel_sigma3.0_16D                   16       0.0000          nan        N/A DEGRADED  
exp_power_beta1.0_16D                 16      11.0904      10.7795     0.3109 OK        
ring_R3.0_w0.3_16D                    16      17.5200     177.4045   159.8845 DEGRADED  
twisted_t1.0_16D                      16       0.0000       0.3823     0.3823 OK        
skew_normal_a5.0_16D                  16       0.0000         FAIL          - FAILED    
bimodal_w0.9_16D                      16       0.0000       0.0002     0.0002 OK        
student_t_nu3.0_24D                   24       5.5392      -2.8455     8.3847 DEGRADED  
student_t_cauchy_24D                  24      -4.4252      -4.4520     0.0268 OK        
banana_b0.1_24D                       24      22.0545      22.0458     0.0087 OK        
funnel_sigma3.0_24D                   24       0.0000          nan        N/A DEGRADED  
exp_power_beta1.0_24D                 24      16.6355       1.1660    15.4696 DEGRADED  
twisted_t1.0_24D                      24       0.0000       0.3822     0.3822 OK        
skew_normal_a5.0_24D                  24       0.0000         FAIL          - FAILED    
bimodal_w0.9_24D                      24       0.0000       0.0002     0.0002 OK        
student_t_nu3.0_32D                   32       3.6916      -7.9475    11.6391 DEGRADED  
student_t_cauchy_32D                  32     -10.3897     -10.4063     0.0166 OK        
banana_b0.1_32D                       32      29.4060      29.3973     0.0087 OK        
funnel_sigma3.0_32D                   32       0.0000          nan        N/A DEGRADED  
exp_power_beta1.0_32D                 32      22.1807      18.0413     4.1394 DEGRADED  
twisted_t1.0_32D                      32       0.0000       0.3818     0.3818 OK        
skew_normal_a5.0_32D                  32       0.0000         FAIL          - FAILED    
bimodal_w0.9_32D                      32       0.0000       0.0002     0.0002 OK        
student_t_nu3.0_48D                   48      -2.6697     -23.4248    20.7550 DEGRADED  
student_t_cauchy_48D                  48     -25.1446     -25.1116     0.0330 OK        
banana_b0.1_48D                       48      44.1090      44.1012     0.0079 OK        
funnel_sigma3.0_48D                   48       0.0000          nan        N/A DEGRADED  
exp_power_beta1.0_48D                 48      33.2711      26.3766     6.8945 DEGRADED  
twisted_t1.0_48D                      48       0.0000       0.3821     0.3821 OK        
skew_normal_a5.0_48D                  48       0.0000         FAIL          - FAILED    
bimodal_w0.9_48D                      48       0.0000       0.0002     0.0002 OK        
student_t_nu3.0_64D                   64     -11.6363     -40.3900    28.7538 DEGRADED  
student_t_cauchy_64D                  64     -42.6175     -42.4883     0.1291 OK        
banana_b0.1_64D                       64      58.8121      58.8038     0.0082 OK        
funnel_sigma3.0_64D                   64       0.0000          nan        N/A DEGRADED  
exp_power_beta1.0_64D                 64      44.3614      92.2818    47.9204 DEGRADED  
twisted_t1.0_64D                      64       0.0000       0.3778     0.3778 OK        
skew_normal_a5.0_64D                  64       0.0000         FAIL          - FAILED    
bimodal_w0.9_64D                      64       0.0000       0.0002     0.0002 OK        
egg_box_omega5.0_2D                    2     236.3128     235.6159     0.6969 OK        
==========================================================================================

SUMMARY STATISTICS
----------------------------------------
Total runs:      75
Successful:      67
Failed:          8

Error statistics (log units):
  Mean:   7.3725
  Median: 0.2497
  Max:    159.8845
  Min:    0.0000

Error breakdown:
  < 0.1 log units:   27 (excellent - Laplace-appropriate)
  0.1 - 1.0:         15 (good - minor degradation)
  1.0 - 10.0:         9 (degraded - significant error)
  > 10.0:             9 (failed - Laplace inappropriate)

Failed runs:
  - skew_normal_a5.0_2D: module 'cupy' has no attribute 'erf'
  - skew_normal_a5.0_4D: module 'cupy' has no attribute 'erf'
  - skew_normal_a5.0_8D: module 'cupy' has no attribute 'erf'
  - skew_normal_a5.0_16D: module 'cupy' has no attribute 'erf'
  - skew_normal_a5.0_24D: module 'cupy' has no attribute 'erf'
  - skew_normal_a5.0_32D: module 'cupy' has no attribute 'erf'
  - skew_normal_a5.0_48D: module 'cupy' has no attribute 'erf'
  - skew_normal_a5.0_64D: module 'cupy' has no attribute 'erf'

==========================================================================================
KEY FINDINGS FOR PAPER
==========================================================================================

Heavy tails: Laplace underestimates tail probability mass:
  Avg error: 4.6957 log units
  Max error: 28.7538 log units
  Status:    ✗ FAILS

Curved degeneracy: mode direction is nonlinear:
  Avg error: 0.0299 log units
  Max error: 0.0922 log units
  Status:    ✓ PASSES

Varying curvature: Hessian changes by exp(v):
  Avg error: 1.1250 log units
  Max error: 1.1250 log units
  Status:    ⚠ DEGRADED

Non-quadratic: |x|^1.0 != x^2:
  Avg error: 9.3873 log units
  Max error: 47.9204 log units
  Status:    ✗ FAILS

Non-quadratic: |x|^0.5 != x^2:
  Avg error: 4.1671 log units
  Max error: 7.1436 log units
  Status:    ⚠ DEGRADED

Saddle point: max probability at r=R but Hessian indefinite:
  Avg error: 68.6035 log units
  Max error: 159.8845 log units
  Status:    ✗ FAILS

Nonlinear correlation: sin(x) dependence:
  Avg error: 0.3816 log units
  Max error: 0.3824 log units
  Status:    ✓ PASSES

Unequal weights: curvature-based weighting fails:
  Avg error: 0.0002 log units
  Max error: 0.0002 log units
  Status:    ✓ PASSES

Many modes: must find and weight all peaks correctly:
  Avg error: 0.6969 log units
  Max error: 0.6969 log units
  Status:    ✓ PASSES
