Details

analyze336.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample29.0ms

Algorithm

intervals

Results

10.0ms	204×	body	80	valid
5.0ms	20×	body	2560	valid
3.0ms	13×	body	1280	valid
2.0ms	7×	body	5120	valid
1.0ms	5×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 36.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.4b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64` `sqrt-prod_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `associate-*r/_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 40

Calls

3 calls:

12.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series168.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
29.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
25.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify129.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4944	847
1	4944	847

prune70.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 14.1b

Counts

50 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
6.8b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
28.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
34×	`sqrt-pow1_binary64`
29×	`pow1_binary64`
28×	`sqrt-div_binary64`
18×	`*-un-lft-identity_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `pow-prod-up_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`frac-times_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 124

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
17.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
34.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
27.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify99.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5001	2259

prune88.0ms

Filtered

72 candidates to 136 candidates (-88.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 14.1b

Counts

143 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
5.1b	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
29.6b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.6b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
9×	`associate-r_binary64`
8×	`sqrt-prod_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64`
2×	`associate-*r/_binary64` `pow1/3_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 65

Calls

4 calls:

10.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
10.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
105.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
82.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
87.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify126.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4934	2208
1	4934	2208

prune94.0ms

Filtered

68 candidates to 77 candidates (-13.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	76	8	84

Merged error: 14.1b

Counts

84 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

29.6b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.6b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.6b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.6b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`cbrt-div_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `pow1/3_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`

Counts

4 → 52

Calls

4 calls:

5.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
86.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
83.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
88.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5005	1172

prune97.0ms

Filtered

60 candidates to 64 candidates (-6.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	64	8	72

Merged error: 14.1b

Counts

72 → 8

regimes139.0ms

Accuracy

50.2% (10.7b remaining)

Error of 28.1b against oracle of 17.4b and baseline of 38.9b

bsearch112.0ms

Steps

Iters	Range		Point
6	8.965066411846153e+72	4.118052215602401e+73	1.9018558815767983e+73
9	6.261490925923726e-300	1.5693821046299034e-291	6.424283181987542e-300
7	-6.5351050775493594e-18	-1.6271732240011801e-19	-1.5994446716436156e-18
10	-3.1973877720294105e+84	-8.279049670379644e+68	-1.5121543370492806e+69

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	69	149
1	69	149

end0.0ms

sample909.0ms

Algorithm

intervals

Results

298.0ms	6096×	body	80	valid
193.0ms	693×	body	2560	valid
110.0ms	460×	body	1280	valid
87.0ms	261×	body	5120	valid
49.0ms	279×	body	640	valid
19.0ms	140×	body	320	valid
6.0ms	71×	body	160	valid

Details

analyze336.0ms

sample29.0ms

simplify12.0ms

prune3.0ms

localize11.0ms

rewrite25.0ms

series168.0ms

simplify129.0ms

prune70.0ms

localize13.0ms

rewrite48.0ms

series117.0ms

simplify99.0ms

prune88.0ms

localize14.0ms

rewrite30.0ms

series405.0ms

simplify126.0ms

prune94.0ms

localize19.0ms

rewrite19.0ms

series342.0ms

simplify88.0ms

prune97.0ms

regimes139.0ms

bsearch112.0ms

simplify5.0ms

end0.0ms

sample909.0ms

Profiling