Details

analyze2.0s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

sample139.0ms

Algorithm

intervals

Results

47.0ms	256×	body	80	valid
35.0ms	252×	body	80	nan
29.0ms	165×	body	80	invalid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5401	35

prune9.0ms

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: 25.2b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

6.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d l) (/.f64 1.0 2.0))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
9.3b	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))
11.5b	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))
13.1b	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log_binary64`
107×	`prod-exp_binary64`
55×	`div-exp_binary64`
45×	`times-frac_binary64`
40×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `pow-exp_binary64`
30×	`add-cbrt-cube_binary64`
26×	`pow-unpow_binary64` `unpow-prod-down_binary64`
16×	`associate-r_binary64`
14×	`pow-to-exp_binary64`
13×	`cbrt-unprod_binary64`
10×	`pow1_binary64`
5×	`cbrt-undiv_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-l_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64` `frac-times_binary64`

Counts

4 → 174

Calls

4 calls:

16.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d l) (/.f64 1.0 2.0))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
6.0ms	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))
15.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))
6.0ms	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))

series590.0ms

Counts

4 → 12

Calls

4 calls:

315.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d l) (/.f64 1.0 2.0))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
14.0ms	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))
247.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))
14.0ms	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4974	3504
1	4974	3504

prune386.0ms

Filtered

111 candidates to 186 candidates (-67.6%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	164	22	186
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	165	22	187

Merged error: 11.8b

Counts

187 → 22

localize42.0ms

Local error

Found 4 expressions with local error:

3.9b	(/.f64 (.f64 M D) (.f64 2.0 d))
6.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1.0 2.0)) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0)) (/.f64 h l))))
9.3b	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))
11.5b	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

738×	`add-exp-log_binary64`
487×	`prod-exp_binary64`
216×	`pow-exp_binary64`
171×	`div-exp_binary64`
78×	`pow-to-exp_binary64`
46×	`add-cbrt-cube_binary64`
28×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
20×	`cbrt-unprod_binary64`
16×	`associate-r_binary64`
13×	`pow-unpow_binary64` `unpow-prod-down_binary64`
9×	`pow1_binary64` `cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `associate-l_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `flip3--_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `flip--_binary64` `frac-times_binary64`

Counts

4 → 258

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
33.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1.0 2.0)) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0)) (/.f64 h l))))
6.0ms	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))
13.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

series590.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
315.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1.0 2.0)) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0)) (/.f64 h l))))
14.0ms	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))
251.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

simplify88.0ms

Algorithm

egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5035	8346

prune338.0ms

Filtered

87 candidates to 270 candidates (-210.3%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	265	5	270
Fresh	0	21	21
Picked	1	0	1
Done	0	0	0
Total	266	26	292

Merged error: 10.5b

Counts

292 → 26

localize56.0ms

Local error

Found 4 expressions with local error:

2.4b	(pow.f64 (/.f64 d (cbrt.f64 h)) (/.f64 1.0 2.0))
3.9b	(/.f64 (.f64 M D) (.f64 2.0 d))
6.8b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0)) (/.f64 h l))))
11.5b	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

6965×	`add-exp-log_binary64`
5245×	`prod-exp_binary64`
2614×	`pow-exp_binary64`
1626×	`div-exp_binary64`
789×	`pow-to-exp_binary64`
232×	`1-exp_binary64` `rec-exp_binary64`
55×	`add-cbrt-cube_binary64`
37×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
27×	`cbrt-unprod_binary64`
22×	`unpow-prod-down_binary64`
16×	`associate-r_binary64`
13×	`pow-unpow_binary64`
12×	`pow1_binary64`
9×	`cbrt-undiv_binary64` `cbrt-prod_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `div-inv_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`sub-neg_binary64` `associate-l_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `flip3--_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `flip--_binary64` `frac-times_binary64`

Counts

4 → 1227

Calls

4 calls:

7.0ms	(pow.f64 (/.f64 d (cbrt.f64 h)) (/.f64 1.0 2.0))
6.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
81.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0)) (/.f64 h l))))
14.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

series678.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(pow.f64 (/.f64 d (cbrt.f64 h)) (/.f64 1.0 2.0))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
375.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0)) (/.f64 h l))))
254.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

simplify340.0ms

Algorithm

egg-herbie

Counts

1239 → 1239

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4973	59670
1	4973	59670

prune448.0ms

Filtered

98 candidates to 1239 candidates (-1164.3%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	1234	5	1239
Fresh	0	25	25
Picked	1	0	1
Done	0	0	0
Total	1235	30	1265

Merged error: 9.1b

Counts

1265 → 30

localize58.0ms

Local error

Found 4 expressions with local error:

3.9b	(/.f64 (.f64 M D) (.f64 2.0 d))
4.9b	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
6.3b	(.f64 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
6.8b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

7347×	`add-exp-log_binary64`
5500×	`prod-exp_binary64`
2652×	`pow-exp_binary64`
1701×	`div-exp_binary64`
796×	`pow-to-exp_binary64`
232×	`1-exp_binary64` `rec-exp_binary64`
95×	`add-cbrt-cube_binary64`
70×	`cbrt-unprod_binary64`
26×	`associate-r_binary64`
23×	`pow1_binary64`
19×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
17×	`cbrt-undiv_binary64`
12×	`pow-prod-down_binary64`
9×	`cbrt-prod_binary64`
7×	`associate-*l/_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r/_binary64` `associate-l_binary64` `-commutative_binary64`
2×	`sub-neg_binary64` `div-inv_binary64`
1×	`associate-/r_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `flip--_binary64` `frac-times_binary64`

Counts

4 → 1280

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
14.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
22.0ms	(.f64 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
83.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

series1.0s

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
181.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
257.0ms	(.f64 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
573.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

simplify389.0ms

Algorithm

egg-herbie

Counts

1292 → 1292

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4982	61073
1	4982	61073

prune219.0ms

Filtered

78 candidates to 1292 candidates (-1556.4%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	1290	2	1292
Fresh	0	29	29
Picked	1	0	1
Done	0	0	0
Total	1291	31	1322

Merged error: 9.1b

Counts

1322 → 31

regimes1.4s

Accuracy

-3.8% (6.4b remaining)

Error of 14.7b against oracle of 8.4b and baseline of 14.5b

bsearch300.0ms

Steps

Iters	Range		Point
7	1.4760170467602473e+108	6.651435636450236e+109	1.5013057695983917e+108
10	1.5321504376458802e-78	1.3638446647950287e-63	1.3343473844226442e-63

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	322	206
1	322	206

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8169×	body	80	nan
875.0ms	4878×	body	80	invalid

Details

analyze2.0s

sample139.0ms

simplify24.0ms

prune9.0ms

localize28.0ms

rewrite52.0ms

series590.0ms

simplify77.0ms

prune386.0ms

localize42.0ms

rewrite80.0ms

series590.0ms

simplify88.0ms

prune338.0ms

localize56.0ms

rewrite331.0ms

series678.0ms

simplify340.0ms

prune448.0ms

localize58.0ms

rewrite359.0ms

series1.0s

simplify389.0ms

prune219.0ms

regimes1.4s

bsearch300.0ms

simplify6.0ms

end0.0ms

sample4.2s

Profiling