Details

analyze7.1s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 15.392003%

Guaranteed chance to sample good point: 24.181524%

sample140.0ms

Algorithm

intervals

Results

50.0ms	61×	body	1280	valid
32.0ms	57×	body	640	valid
14.0ms	100×	body	80	valid
12.0ms	28×	body	320	valid
6.0ms	49×	body	80	invalid
4.0ms	6×	body	640	invalid
3.0ms	10×	body	160	valid
2.0ms	4×	body	320	invalid
1.0ms	2×	body	160	invalid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	13
1	158	13
2	903	13
3	5001	13

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 35.0b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (/ (pow t 3.0) (* l l)) (sin k))
3.4b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.8b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
19.5b	(/ (pow t 3.0) (* l l))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log`
58×	`prod-exp`
52×	`add-cbrt-cube`
26×	`cbrt-unprod`
24×	`div-exp`
21×	`add-sqr-sqrt`
20×	`pow1`
19×	`*-un-lft-identity`
17×	`times-frac`
16×	`associate-*l/`
14×	`add-cube-cbrt`
13×	`associate-l`
11×	`associate-r`
10×	`frac-times` `unpow-prod-down` `pow-prod-down`
8×	`tan-quot` `cbrt-undiv` `pow-to-exp` `pow-exp`
7×	`associate-/l*`
6×	`associate-*r/`
4×	`flip3-+` `flip-+` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r*`

Counts

4 → 144

Calls

4 calls:

9.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
11.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
22.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
6.0ms	(/ (pow t 3.0) (* l l))

series325.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
71.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
157.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
40.0ms	(/ (pow t 3.0) (* l l))

simplify119.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	857	1728
1	4784	1448
2	5001	1444

prune332.0ms

Filtered

96 candidates to 156 candidates (-62.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	142	14	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	14	157

Merged error: 23.6b

Counts

157 → 14

localize230.0ms

Local error

Found 4 expressions with local error:

2.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.4b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
10.5b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
14.8b	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

304×	`add-exp-log`
184×	`prod-exp`
78×	`add-cbrt-cube`
77×	`div-exp`
50×	`add-sqr-sqrt`
49×	`times-frac`
44×	`associate-*l/` `cbrt-unprod`
42×	`*-un-lft-identity`
37×	`add-cube-cbrt`
36×	`associate-l`
34×	`frac-times`
33×	`pow-exp`
29×	`pow1`
24×	`unpow-prod-down`
22×	`pow-to-exp`
17×	`pow-prod-down`
16×	`tan-quot`
14×	`associate-*r/`
12×	`cbrt-undiv`
11×	`associate-r`
10×	`cbrt-prod`
8×	`flip3-+` `flip-+` `sqr-pow`
5×	`associate-/l*` `unswap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 229

Calls

4 calls:

11.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
16.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
31.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series349.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
80.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
41.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
175.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1430	3890
1	5002	3397

prune577.0ms

Filtered

152 candidates to 241 candidates (-58.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	233	8	241
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	238	17	255

Merged error: 17.8b

Counts

255 → 17

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
2.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.4b	(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
14.8b	(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

2085×	`add-exp-log`
1365×	`prod-exp`
627×	`div-exp`
253×	`add-cbrt-cube`
210×	`pow-to-exp` `pow-exp`
187×	`cbrt-unprod`
116×	`associate-*l/`
98×	`frac-times`
57×	`cbrt-undiv`
50×	`pow1`
43×	`add-sqr-sqrt`
36×	`associate-l`
35×	`*-un-lft-identity`
34×	`times-frac`
33×	`pow-prod-down`
32×	`tan-quot`
30×	`add-cube-cbrt` `associate-*r/`
26×	`unpow-prod-down`
16×	`flip3-+` `flip-+`
13×	`cbrt-prod`
11×	`associate-r`
5×	`unswap-sqr` `sqr-pow`
4×	`add-log-exp`
3×	`pow-unpow` `*-commutative` `distribute-lft-out`
2×	`pow-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `div-inv`

Counts

4 → 518

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
11.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
36.0ms	(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
60.0ms	(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series366.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(pow (cbrt t) 3.0)
54.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
84.0ms	(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
182.0ms	(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify146.0ms

Algorithm

egg-herbie

Counts

530 → 530

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2615	12493
1	5001	11859

prune922.0ms

Filtered

189 candidates to 530 candidates (-180.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	516	14	530
Fresh	8	8	16
Picked	1	0	1
Done	0	0	0
Total	525	22	547

Merged error: 17.2b

Counts

547 → 22

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
0.7b	(pow (cbrt t) 3.0)
2.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
17.9b	(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

2084×	`add-exp-log`
1364×	`prod-exp`
627×	`div-exp`
251×	`add-cbrt-cube`
211×	`pow-to-exp` `pow-exp`
186×	`cbrt-unprod`
81×	`frac-times`
70×	`associate-*l/`
57×	`cbrt-undiv`
49×	`pow1`
44×	`add-sqr-sqrt`
39×	`associate-*r/`
35×	`associate-l`
34×	`times-frac`
32×	`unpow-prod-down` `pow-prod-down`
31×	`add-cube-cbrt` `*-un-lft-identity`
24×	`tan-quot`
16×	`cbrt-prod` `flip3-+` `flip-+`
6×	`pow-unpow` `sqr-pow`
5×	`unswap-sqr`
4×	`distribute-rgt-in` `pow-pow` `distribute-lft-in` `associate-r` `add-log-exp`
2×	`pow1/3` `*-commutative`
1×	`div-inv`

Counts

4 → 507

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
3.0ms	(pow (cbrt t) 3.0)
11.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
51.0ms	(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow (cbrt t) 3.0)
45.0ms	(pow (cbrt t) 3.0)
54.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
179.0ms	(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify144.0ms

Algorithm

egg-herbie

Counts

519 → 519

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2542	13036
1	5002	12901

prune728.0ms

Filtered

173 candidates to 519 candidates (-200.0%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	513	6	519
Fresh	8	13	21
Picked	1	0	1
Done	0	0	0
Total	522	19	541

Merged error: 15.7b

Counts

541 → 19

Details

analyze7.1s

sample140.0ms

simplify29.0ms

prune4.0ms

localize20.0ms

rewrite53.0ms

series325.0ms

simplify119.0ms

prune332.0ms

localize230.0ms

rewrite79.0ms

series349.0ms

simplify64.0ms

prune577.0ms

localize32.0ms

rewrite169.0ms

series366.0ms

simplify146.0ms

prune922.0ms

localize29.0ms

rewrite126.0ms

series325.0ms

simplify144.0ms

prune728.0ms

regimes662.0ms

bsearch3.0ms

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