Details

analyze2.1s

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

sample156.0ms

Algorithm

intervals

Results

48.0ms	256×	body	80	valid
44.0ms	311×	body	80	nan
30.0ms	170×	body	80	invalid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5401	35

prune10.0ms

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: 29.3b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

7.9b	(.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))))
11.3b	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))
12.8b	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))
13.5b	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))

rewrite53.0ms

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:

17.0ms	(.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))))
9.0ms	(pow.f64 (/.f64 d l) (/.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))
6.0ms	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))

series589.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(.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 l) (/.f64 1.0 2.0))
244.0ms	(.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 h) (/.f64 1.0 2.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4974	3504
1	4974	3504

prune407.0ms

Filtered

110 candidates to 186 candidates (-69.1%)

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: 12.4b

Counts

187 → 22

localize42.0ms

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (.f64 M D) (.f64 2.0 d))
7.9b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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))))
11.3b	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))
12.8b	(.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))
34.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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 l) (/.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))

series586.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
318.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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 l) (/.f64 1.0 2.0))
246.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

simplify91.0ms

Algorithm

egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5028	8328

prune348.0ms

Filtered

89 candidates to 270 candidates (-203.4%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	260	10	270
Fresh	6	15	21
Picked	1	0	1
Done	0	0	0
Total	267	25	292

Merged error: 11.6b

Counts

292 → 25

localize59.0ms

Local error

Found 4 expressions with local error:

2.6b	(pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0))
4.0b	(/.f64 (.f64 M D) (.f64 2.0 d))
7.9b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.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))))
12.8b	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

rewrite318.0ms

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 l)) (/.f64 1.0 2.0))
6.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
81.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.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))))
13.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

series683.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
394.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.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))))
243.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

simplify360.0ms

Algorithm

egg-herbie

Counts

1239 → 1239

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5087	59653

prune449.0ms

Filtered

97 candidates to 1239 candidates (-1177.3%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	1233	6	1239
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	1236	28	1264

Merged error: 10.3b

Counts

1264 → 28

localize61.0ms

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (.f64 M D) (.f64 2.0 d))
5.7b	(.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)))
6.6b	(/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (*.f64 2.0 l))
7.9b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (.f64 2.0 l))))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

6936×	`add-exp-log_binary64`
5237×	`prod-exp_binary64`
2607×	`pow-exp_binary64`
1610×	`div-exp_binary64`
787×	`pow-to-exp_binary64`
232×	`1-exp_binary64` `rec-exp_binary64`
60×	`add-cbrt-cube_binary64`
29×	`cbrt-unprod_binary64`
11×	`pow1_binary64`
10×	`cbrt-undiv_binary64`
8×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
6×	`associate-r_binary64` `add-cube-cbrt_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-l_binary64`
2×	`associate-/r_binary64` `sub-neg_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `-commutative_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 1180

Calls

4 calls:

15.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
8.0ms	(.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)))
11.0ms	(/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (*.f64 2.0 l))
85.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (.f64 2.0 l))))

series730.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
117.0ms	(.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)))
209.0ms	(/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (*.f64 2.0 l))
397.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (.f64 2.0 l))))

simplify351.0ms

Algorithm

egg-herbie

Counts

1192 → 1192

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5057	58967

prune189.0ms

Filtered

63 candidates to 1192 candidates (-1792.1%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	1187	5	1192
Fresh	3	24	27
Picked	1	0	1
Done	0	0	0
Total	1191	29	1220

Merged error: 10.0b

Counts

1220 → 29

regimes1.4s

Accuracy

17.6% (5.0b remaining)

Error of 14.5b against oracle of 9.5b and baseline of 15.5b

bsearch244.0ms

Steps

Iters	Range		Point
8	3.9036749666279574e-08	0.0021857205059727662	5.468046365784226e-08
6	-1.5630454568252133e+119	-9.999860355383097e+117	-2.5203757008157784e+118

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	160	141
1	160	141

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8617×	body	80	nan
897.0ms	4888×	body	80	invalid

Details

analyze2.1s

sample156.0ms

simplify23.0ms

prune10.0ms

localize29.0ms

rewrite53.0ms

series589.0ms

simplify84.0ms

prune407.0ms

localize42.0ms

rewrite80.0ms

series586.0ms

simplify91.0ms

prune348.0ms

localize59.0ms

rewrite318.0ms

series683.0ms

simplify360.0ms

prune449.0ms

localize61.0ms

rewrite331.0ms

series730.0ms

simplify351.0ms

prune189.0ms

regimes1.4s

bsearch244.0ms

simplify4.0ms

end0.0ms

sample4.3s

Profiling