Details

analyze1.4s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample235.0ms

Algorithm

intervals

Results

160.0ms	58×	body	2560	valid
37.0ms	81×	body	1280	valid
18.0ms	65×	body	640	valid
4.0ms	22×	body	320	valid
2.0ms	21×	body	80	valid
1.0ms	9×	body	160	valid

simplify448.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

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: 28.7b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.7b	(- x (tan x))
0.7b	(- x (sin x))

rewrite20.0ms

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 → 78

Calls

3 calls:

7.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series50.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
13.0ms	(- x (sin x))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5236	1127

prune90.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Merged error: 0.0b

Counts

88 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(- x (tan x))
0.7b	(- x (sin x))
0.7b	(- x (sin x))
0.7b	(- x (sin x))

rewrite18.0ms

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 → 52

Calls

4 calls:

3.0ms	(- x (tan x))
6.0ms	(- x (sin x))
4.0ms	(- x (sin x))
4.0ms	(- x (sin x))

series24.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- x (tan x))
4.0ms	(- x (sin x))
5.0ms	(- x (sin x))
5.0ms	(- x (sin x))

simplify35.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5345	498

prune71.0ms

Filtered

49 candidates to 64 candidates (-30.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	64	3	67

Merged error: 0.0b

Counts

67 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* x (* x 9/40))
0.1b	(* x 9/40)
18.6b	(- (* x (* x 9/40)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

5.0ms	(* 27/2800 (pow x 4))
4.0ms	(* x (* x 9/40))
3.0ms	(* x 9/40)
7.0ms	(- (* x (* x 9/40)) (+ (* 27/2800 (pow x 4)) 1/2))

series17.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* 27/2800 (pow x 4))
3.0ms	(* x (* x 9/40))
2.0ms	(* x 9/40)
6.0ms	(- (* x (* x 9/40)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify46.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4939	656
1	4939	656

prune99.0ms

Filtered

52 candidates to 86 candidates (-65.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	86	3	89

Merged error: 0b

Counts

89 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* x (* x 9/40))
0.1b	(* x 9/40)
18.6b	(- (* x (* x 9/40)) (* 27/2800 (pow x 4)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`pow1` `associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
7×	`prod-exp`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--`

Counts

4 → 72

Calls

4 calls:

5.0ms	(* 27/2800 (pow x 4))
6.0ms	(* x (* x 9/40))
3.0ms	(* x 9/40)
4.0ms	(- (* x (* x 9/40)) (* 27/2800 (pow x 4)))

series18.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 27/2800 (pow x 4))
3.0ms	(* x (* x 9/40))
2.0ms	(* x 9/40)
9.0ms	(- (* x (* x 9/40)) (* 27/2800 (pow x 4)))

simplify49.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4860	579
1	4860	579

prune93.0ms

Filtered

51 candidates to 84 candidates (-64.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	84	3	87

Merged error: 0b

Counts

87 → 3

regimes103.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.0b

bsearch55.0ms

Steps

Iters	Range		Point
9	0.0016915916628197601	130.20461435039707	0.033556415281753814
9	-19.681296786070995	-7.012671180892342e-07	-0.029261909414358904

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	31
1	28	31

end0.0ms

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample6.6s

Algorithm

intervals

Results

3.9s	1553×	body	2560	valid
1.7s	2740×	body	1280	valid
523.0ms	1904×	body	640	valid
174.0ms	924×	body	320	valid
64.0ms	468×	body	160	valid
32.0ms	411×	body	80	valid

Details

analyze1.4s

sample235.0ms

simplify448.0ms

prune4.0ms

localize11.0ms

rewrite20.0ms

series50.0ms

simplify45.0ms

prune90.0ms

localize13.0ms

rewrite18.0ms

series24.0ms

simplify35.0ms

prune71.0ms

localize9.0ms

rewrite21.0ms

series17.0ms

simplify46.0ms

prune99.0ms

localize9.0ms

rewrite21.0ms

series18.0ms

simplify49.0ms

prune93.0ms

regimes103.0ms

bsearch55.0ms

simplify1.0ms

end0.0ms

analyze1.1s

sample6.6s

Profiling