Details

sample488.0ms

Algorithm

intervals

Results

162.0ms	57×	body	2560	valid
53.0ms	81×	body	1280	valid
16.0ms	58×	body	640	valid
6.0ms	31×	body	320	valid
3.0ms	19×	body	160	valid
1.0ms	10×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 33.2b

Counts

2 → 1

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.8b	(- x (sin x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series172.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
39.0ms	(- x (sin x))

simplify150.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune185.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 9/40 (pow x 2))
0.3b	(* 27/2800 (pow x 4))
15.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 9/40 (pow x 2))
5.0ms	(* 27/2800 (pow x 4))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series107.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 9/40 (pow x 2))
38.0ms	(* 27/2800 (pow x 4))
44.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify43.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5002	315

prune119.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	75	4	79

Merged error: 0.0b

Counts

79 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.7b	(- x (tan x))
1.7b	(- x (tan x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

6.0ms	(/ (sin x) (- x (tan x)))
28.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series331.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (sin x) (- x (tan x)))
171.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
51.0ms	(- x (tan x))
49.0ms	(- x (tan x))

simplify40.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	872
2	5001	872

prune203.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	106	4	110

Merged error: 0.0b

Counts

110 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

1.7b	(- x (tan x))
1.8b	(- x (sin x))
1.8b	(- x (sin x))
1.8b	(- x (sin x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

3.0ms	(- x (tan x))
4.0ms	(- x (sin x))
4.0ms	(- x (sin x))
4.0ms	(- x (sin x))

series148.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- x (tan x))
30.0ms	(- x (sin x))
30.0ms	(- x (sin x))
35.0ms	(- x (sin x))

simplify68.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	150	309
1	342	289
2	774	289
3	2023	289
4	5001	289

prune161.0ms

Filtered

68 candidates to 49 candidates (72.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

regimes59.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch75.0ms

Steps

Iters	Range		Point
9	8.159003009805276e-07	0.06291072096871789	0.026837057201601722
9	-5.855776674212404	-7.74497267090904e-05	-0.02703430163315367

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	34
1	33	34

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.9s	1552×	body	2560	valid
1.7s	2752×	body	1280	valid
514.0ms	1941×	body	640	valid
163.0ms	897×	body	320	valid
64.0ms	490×	body	160	valid
27.0ms	368×	body	80	valid