Details

analyze2.0s (6.4%)

Algorithm

1×

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

sample145.0ms (0.5%)

Algorithm

1×

intervals

Results

49.0ms	256×	body	80	valid
35.0ms	252×	body	80	nan
29.0ms	165×	body	80	invalid

simplify27.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5401	35

prune12.0ms (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

localize30.0ms (0.1%)

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))

rewrite55.0ms (0.2%)

Algorithm

1×	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:

18.0ms	(.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	(.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))
6.0ms	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))

series620.0ms (2%)

Counts

4 → 12

Calls

4 calls:

335.0ms	(.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))))
254.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))
16.0ms	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))
15.0ms	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))

simplify92.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4974	3504
1	4974	3504

prune586.0ms (1.9%)

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

localize46.0ms (0.2%)

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))

rewrite91.0ms (0.3%)

Algorithm

1×	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:

41.0ms	(.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	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
6.0ms	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))

series624.0ms (2%)

Counts

4 → 12

Calls

4 calls:

336.0ms	(.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))))
265.0ms	(.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))
8.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))

simplify106.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5035	8346

prune869.0ms (2.8%)

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

localize58.0ms (0.2%)

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))

rewrite332.0ms (1.1%)

Algorithm

1×	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:

88.0ms	(.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))))
17.0ms	(pow.f64 (/.f64 d (cbrt.f64 h)) (/.f64 1.0 2.0))
14.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))

series691.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

383.0ms	(.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))))
260.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))
40.0ms	(pow.f64 (/.f64 d (cbrt.f64 h)) (/.f64 1.0 2.0))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))

simplify374.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1239 → 1239

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4973	59670
1	4973	59670

prune8.5s (27.5%)

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

localize56.0ms (0.2%)

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))))

rewrite352.0ms (1.1%)

Algorithm

1×	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:

84.0ms	(.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))))
30.0ms	(.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))
15.0ms	(.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)))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))

series822.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

381.0ms	(.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))))
255.0ms	(.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))
180.0ms	(.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)))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))

simplify625.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1292 → 1292

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4982	61073
1	4982	61073

prune7.8s (25.2%)

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 (4.6%)

Accuracy

Total 6.4b remaining (43.3%)

Threshold costs 0b (0%)

bsearch298.0ms (1%)

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 (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	322	206
1	322	206

end0.0ms (0%)

sample4.3s (13.9%)

Algorithm

1×

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8169×	body	80	nan
903.0ms	4878×	body	80	invalid

Details

analyze2.0s (6.4%)

sample145.0ms (0.5%)

simplify27.0ms (0.1%)

prune12.0ms (0%)

localize30.0ms (0.1%)

rewrite55.0ms (0.2%)

series620.0ms (2%)

simplify92.0ms (0.3%)

prune586.0ms (1.9%)

localize46.0ms (0.2%)

rewrite91.0ms (0.3%)

series624.0ms (2%)

simplify106.0ms (0.3%)

prune869.0ms (2.8%)

localize58.0ms (0.2%)

rewrite332.0ms (1.1%)

series691.0ms (2.2%)

simplify374.0ms (1.2%)

prune8.5s (27.5%)

localize56.0ms (0.2%)

rewrite352.0ms (1.1%)

series822.0ms (2.7%)

simplify625.0ms (2%)

prune7.8s (25.2%)

regimes1.4s (4.6%)

bsearch298.0ms (1%)

simplify6.0ms (0%)

end0.0ms (0%)

sample4.3s (13.9%)

Profiling