Details

sample492.0ms

Algorithm

intervals

Results

146.0ms	52×	body	2560	valid
62.0ms	89×	body	1280	valid
16.0ms	62×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	11×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune4.0ms

Filtered

1 candidates to 0 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: 32.8b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`flip3--` `flip--`
2×	`sub-neg` `associate-/r/` `associate-/l/`
1×	`frac-2neg` `div-sub` `clear-num` `div-inv`

Counts

3 → 16

Calls

3 calls:

4.0ms	(/ (- x (sin x)) (- x (tan x)))
2.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series187.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- x (sin x)) (- x (tan x)))
52.0ms	(- x (tan x))
55.0ms	(- x (sin x))

simplify61.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	208	173
1	666	172
2	2154	172
3	5001	170

prune79.0ms

Filtered

25 candidates to 19 candidates (76.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	4	26

Merged error: 0.0b

Counts

26 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
15.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-r`
2×	`*-commutative` `associate--r+` `sqr-pow`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `unpow2`

Counts

3 → 11

Calls

3 calls:

3.0ms	(* 27/2800 (pow x 4))
3.0ms	(* 9/40 (pow x 2))
6.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series109.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* 27/2800 (pow x 4))
29.0ms	(* 9/40 (pow x 2))
44.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify83.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	99	92
1	386	90
2	1705	90
3	5001	90

prune42.0ms

Filtered

20 candidates to 10 candidates (50.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	20	4	24

Merged error: 0.0b

Counts

24 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
15.8b	(- (- (* 9/40 (pow x 2)) 1/2) (* 27/2800 (pow x 4)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-r`
2×	`sub-neg` `associate--l+` `*-commutative` `sqr-pow`
1×	`associate--l-` `flip3--` `flip--` `unpow2`

Counts

3 → 12

Calls

3 calls:

3.0ms	(* 27/2800 (pow x 4))
3.0ms	(* 9/40 (pow x 2))
6.0ms	(- (- (* 9/40 (pow x 2)) 1/2) (* 27/2800 (pow x 4)))

series105.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* 27/2800 (pow x 4))
23.0ms	(* 9/40 (pow x 2))
47.0ms	(- (- (* 9/40 (pow x 2)) 1/2) (* 27/2800 (pow x 4)))

simplify66.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	93	95
1	302	93
2	1435	90
3	5001	90

prune43.0ms

Filtered

21 candidates to 11 candidates (52.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	21	4	25

Merged error: 0.0b

Counts

25 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.9b	(- x (tan x))
1.9b	(- x (tan x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`frac-2neg` `frac-sub`
7×	`clear-num`
6×	`flip3--` `associate-/r/` `flip--`
3×	`sub-neg` `distribute-rgt-out--` `div-inv`
2×	`sub-div`

Counts

4 → 31

Calls

4 calls:

3.0ms	(/ (sin x) (- x (tan x)))
7.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.0ms	(- x (tan x))
2.0ms	(- x (tan x))

series346.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (sin x) (- x (tan x)))
178.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
55.0ms	(- x (tan x))
52.0ms	(- x (tan x))

simplify38.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	332	441
1	1211	414
2	5001	411

prune98.0ms

Filtered

43 candidates to 34 candidates (79.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	43	4	47

Merged error: 0.0b

Counts

47 → 4

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch67.0ms

Steps

Iters	Range		Point
9	2.5653698016906928e-06	357.20278190505735	0.02550642089016014
7	-0.6319501064166059	-0.005814372128176944	-0.030466604001346206

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	29	14

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.6s	1573×	body	2560	valid
1.6s	2832×	body	1280	valid
454.0ms	1870×	body	640	valid
144.0ms	926×	body	320	valid
53.0ms	471×	body	160	valid
22.0ms	328×	body	80	valid