Details

analyze2.4s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

sample136.0ms

Algorithm

intervals

Results

52.0ms	65×	body	1280	valid
34.0ms	55×	body	640	valid
14.0ms	106×	body	80	valid
7.0ms	17×	body	320	valid
5.0ms	41×	body	80	invalid
3.0ms	13×	body	160	valid
3.0ms	8×	body	320	invalid
1.0ms	2×	body	640	invalid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	160	invalid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5086	25

prune18.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 30.3b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.9b	(* (/ (pow t 3.0) (* l l)) (sin k))
12.1b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.9b	(/ (pow t 3.0) (* l l))

rewrite52.0ms

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:

10.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.0ms	(* (/ (pow t 3.0) (* l l)) (sin 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))

series336.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
54.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
164.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
42.0ms	(/ (pow t 3.0) (* l l))

simplify42.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5390	2634

prune296.0ms

Filtered

98 candidates to 156 candidates (-59.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	148	8	156
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	148	10	158

Merged error: 20.5b

Counts

158 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

3.1b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.7b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
9.0b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.1b	(* (* (* (/ (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))

rewrite78.0ms

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)
30.0ms	(* (* (* (/ (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))

series363.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (/ (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))
43.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
186.0ms	(* (* (* (/ (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))

simplify66.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5523	5683

prune545.0ms

Filtered

138 candidates to 241 candidates (-74.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	230	11	241
Fresh	1	7	8
Picked	1	0	1
Done	1	0	1
Total	233	18	251

Merged error: 15.7b

Counts

251 → 18

localize31.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
3.1b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.7b	(* (* (* (/ (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))
12.1b	(* (* (* (* (/ (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))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

2898×	`add-exp-log`
1826×	`prod-exp`
939×	`div-exp`
340×	`add-cbrt-cube`
313×	`pow-to-exp` `pow-exp`
246×	`cbrt-unprod`
125×	`associate-*l/`
103×	`frac-times`
85×	`cbrt-undiv`
61×	`pow1`
41×	`pow-prod-down`
40×	`add-sqr-sqrt`
37×	`associate-l`
34×	`times-frac`
33×	`associate-*r/`
32×	`tan-quot` `*-un-lft-identity`
27×	`add-cube-cbrt`
20×	`unpow-prod-down`
16×	`flip3-+` `flip-+`
12×	`associate-r`
10×	`cbrt-prod`
5×	`unswap-sqr`
4×	`*-commutative` `add-log-exp` `sqr-pow`
3×	`distribute-lft-out`
1×	`distribute-rgt-in` `distribute-lft-in` `div-inv`

Counts

4 → 684

Calls

4 calls:

28.0ms	(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
10.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
41.0ms	(* (* (* (/ (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))
54.0ms	(* (* (* (* (/ (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))

series401.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
55.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
83.0ms	(* (* (* (/ (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))
196.0ms	(* (* (* (* (/ (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))

simplify177.0ms

Algorithm

egg-herbie

Counts

696 → 696

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5032	14241

prune620.0ms

Filtered

161 candidates to 696 candidates (-332.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	688	8	696
Fresh	6	11	17
Picked	1	0	1
Done	0	0	0
Total	695	19	714

Merged error: 14.7b

Counts

714 → 19

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
1.6b	(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
3.1b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.5b	(* (* (* (/ (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 (+ 1.0 (pow (/ k t) 2.0)))))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

2897×	`add-exp-log`
1825×	`prod-exp`
939×	`div-exp`
338×	`add-cbrt-cube`
314×	`pow-to-exp` `pow-exp`
245×	`cbrt-unprod`
86×	`frac-times`
85×	`cbrt-undiv`
79×	`associate-*l/`
60×	`pow1`
42×	`associate-*r/`
41×	`add-sqr-sqrt`
40×	`pow-prod-down`
36×	`associate-l`
34×	`times-frac`
28×	`add-cube-cbrt` `*-un-lft-identity`
26×	`unpow-prod-down`
24×	`tan-quot`
16×	`flip3-+` `flip-+`
13×	`cbrt-prod`
5×	`associate-r` `unswap-sqr` `sqr-pow`
4×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
3×	`pow-unpow` `*-commutative`
2×	`pow-pow`
1×	`pow1/3` `div-inv`

Counts

4 → 673

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
27.0ms	(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
11.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
52.0ms	(* (* (* (/ (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 (+ 1.0 (pow (/ k t) 2.0)))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow (cbrt t) 3.0)
66.0ms	(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
53.0ms	(* (/ (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 (+ 1.0 (pow (/ k t) 2.0)))))

simplify194.0ms

Algorithm

egg-herbie

Counts

685 → 685

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5106	15413

prune471.0ms

Filtered

148 candidates to 685 candidates (-362.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	682	3	685
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	685	19	704

Merged error: 14.7b

Counts

704 → 19

regimes628.0ms

Accuracy

1.9% (3.1b remaining)

Error of 17.8b against oracle of 14.8b and baseline of 17.9b

bsearch2.1s

Steps

Iters	Range		Point
9	2.00489077873161e-88	2.0754866865677187e-82	9.759191564357316e-84
8	-7.799368182073058e+22	-2.700236230311684e+18	-4.278232628469712e+22

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	144
1	64	144

end0.0ms

analyze2.2s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

sample4.0s

Algorithm

intervals

Results

1.6s	2016×	body	1280	valid
883.0ms	1566×	body	640	valid
463.0ms	3327×	body	80	valid
300.0ms	728×	body	320	valid
191.0ms	1397×	body	80	invalid
107.0ms	363×	body	160	valid
66.0ms	120×	body	640	invalid
48.0ms	123×	body	320	invalid
28.0ms	92×	body	160	invalid
17.0ms	22×	body	1280	invalid

Details

analyze2.4s

sample136.0ms

simplify24.0ms

prune18.0ms

localize20.0ms

rewrite52.0ms

series336.0ms

simplify42.0ms

prune296.0ms

localize30.0ms

rewrite78.0ms

series363.0ms

simplify66.0ms

prune545.0ms

localize31.0ms

rewrite227.0ms

series401.0ms

simplify177.0ms

prune620.0ms

localize32.0ms

rewrite180.0ms

series346.0ms

simplify194.0ms

prune471.0ms

regimes628.0ms

bsearch2.1s

simplify2.0ms

end0.0ms

analyze2.2s

sample4.0s

Profiling