Details

sample469.0ms

Algorithm

intervals

Results

131.0ms	64×	body	2560	valid
49.0ms	91×	body	1280	valid
13.0ms	50×	body	640	valid
5.0ms	26×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	10×	body	80	valid

simplify12.0ms

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: 33.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (tan x))
0.9b	(- x (sin x))

rewrite13.0ms

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))
5.0ms	(- x (sin x))

series189.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
57.0ms	(- x (sin x))

simplify66.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (59.0ms)

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

prune70.0ms

Filtered

25 candidates to 19 candidates (76.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Merged error: 0.1b

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))
16.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite12.0ms

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))

series110.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 27/2800 (pow x 4))
28.0ms	(* 9/40 (pow x 2))
46.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify84.0ms

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

prune36.0ms

Filtered

20 candidates to 10 candidates (50.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	20	4	24

Merged error: 0.1b

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))
16.1b	(- (- (* 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)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* 27/2800 (pow x 4))
25.0ms	(* 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 (12.0ms)

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

prune34.0ms

Filtered

21 candidates to 11 candidates (52.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	21	4	25

Merged error: 0.1b

Counts

25 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.8b	(- (* x x) (* (tan x) (tan x)))
0.9b	(- x (sin x))
15.0b	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-commutative`
8×	`difference-of-squares`
4×	`tan-quot` `associate-/l*`
3×	`flip3--` `flip--`
2×	`sub-neg` `associate-/r/` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `associate-l/` `clear-num` `flip-+` `div-inv`

Counts

4 → 29

Calls

4 calls:

3.0ms	(* (tan x) (tan x))
4.0ms	(- (* x x) (* (tan x) (tan x)))
2.0ms	(- x (sin x))
7.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (tan x) (tan x))
85.0ms	(- (* x x) (* (tan x) (tan x)))
34.0ms	(- x (sin x))
146.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

simplify93.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	242	242
1	816	236
2	2789	228
3	5001	227

prune80.0ms

Filtered

41 candidates to 25 candidates (61.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	41	4	45

Merged error: 0.1b

Counts

45 → 4

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.2b

bsearch61.0ms

Steps

Iters	Range		Point
6	0.018000635171863108	0.09117784756913819	0.027293184248221757
10	-1421.6155834850151	-1.485944467815708e-07	-0.026678702825547893

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	11
1	28	11

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.9s	1643×	body	2560	valid
1.5s	2762×	body	1280	valid
476.0ms	1826×	body	640	valid
156.0ms	912×	body	320	valid
57.0ms	483×	body	160	valid
27.0ms	374×	body	80	valid