Details

analyze345.0ms

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

sample35.0ms

Algorithm

intervals

Results

13.0ms	198×	body	80	valid
7.0ms	25×	body	2560	valid
3.0ms	11×	body	1280	valid
2.0ms	7×	body	5120	valid
2.0ms	10×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune4.0ms

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: 38.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.5b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

5.0ms	(+.f64 (.f64 re re) (.f64 im im))
8.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 (.f64 re re) (.f64 im im))
29.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4967	687
1	4967	687

prune63.0ms

Filtered

53 candidates to 63 candidates (-18.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	5	64

Merged error: 16.4b

Counts

64 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.4b	(sqrt.f64 (.f64 (.f64 im im) 2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
37×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
11×	`pow1_binary64`
9×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
4×	`sqrt-pow1_binary64` `associate-/l*_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64`
2×	`pow1/2_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 105

Calls

4 calls:

14.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

series45.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

simplify84.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4958	2290
1	4958	2290

prune77.0ms

Filtered

84 candidates to 117 candidates (-39.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	114	8	122

Merged error: 8.9b

Counts

122 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
0.3b	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
29.7b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

156×	`sqrt-prod_binary64`
142×	`add-sqr-sqrt_binary64`
112×	`times-frac_binary64`
99×	`*-un-lft-identity_binary64`
71×	`add-cube-cbrt_binary64`
60×	`associate-r_binary64`
28×	`difference-of-squares_binary64`
14×	`distribute-lft-out--_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-/r*_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64` `sqrt-div_binary64`
5×	`unswap-sqr_binary64`
4×	`associate-/r/_binary64`
3×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `sqrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

4 → 195

Calls

4 calls:

24.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
12.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
23.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
6.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

simplify64.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4969	3986
1	4969	3986

prune107.0ms

Filtered

111 candidates to 207 candidates (-86.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	202	5	207
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	205	10	215

Merged error: 1.7b

Counts

215 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
0.2b	(.f64 (fabs.f64 im) (sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
29.7b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64`
60×	`sqrt-prod_binary64`
41×	`*-un-lft-identity_binary64`
38×	`times-frac_binary64`
27×	`associate-r_binary64` `add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64`
8×	`pow1_binary64`
7×	`distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r/_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `associate-l_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

4 → 110

Calls

4 calls:

10.0ms	(sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
16.0ms	(.f64 (fabs.f64 im) (sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
31.0ms	(.f64 (fabs.f64 im) (sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
7.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
6.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

simplify46.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4983	2079
1	4983	2079

prune69.0ms

Filtered

90 candidates to 122 candidates (-35.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	121	11	132

Merged error: 1.7b

Counts

132 → 11

regimes256.0ms

Accuracy

40.8% (20.6b remaining)

Error of 23.1b against oracle of 2.5b and baseline of 37.2b

bsearch128.0ms

Steps

Iters	Range		Point
9	2.0956686038457227e+116	3.2551655494341425e+122	2.6357224810606306e+116
7	4.00309387791329e-163	8.593568001402905e-162	1.8553121509605384e-162
6	4.059173426342869e-179	4.314065622770995e-178	8.731569751909133e-179
7	1.2471739354781702e-199	1.6353546386860062e-197	1.1743424555098952e-197
8	-1.0493850288501458e-256	-4.5427166224783115e-260	-4.06564811773753e-259
7	-4.871034871562344e+154	-2.516184961325803e+152	-3.4810819035158894e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	104
1	80	104

end0.0ms

sample958.0ms

Algorithm

intervals

Results

302.0ms	6065×	body	80	valid
204.0ms	692×	body	2560	valid
113.0ms	463×	body	1280	valid
104.0ms	281×	body	5120	valid
58.0ms	286×	body	640	valid
20.0ms	141×	body	320	valid
7.0ms	72×	body	160	valid

Details

analyze345.0ms

sample35.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite27.0ms

series48.0ms

simplify63.0ms

prune63.0ms

localize12.0ms

rewrite35.0ms

series45.0ms

simplify84.0ms

prune77.0ms

localize13.0ms

rewrite61.0ms

series66.0ms

simplify64.0ms

prune107.0ms

localize12.0ms

rewrite43.0ms

series67.0ms

simplify46.0ms

prune69.0ms

regimes256.0ms

bsearch128.0ms

simplify3.0ms

end0.0ms

sample958.0ms

Profiling