Details

analyze1.3s

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

sample230.0ms

Algorithm

intervals

Results

140.0ms	47×	body	2560	valid
51.0ms	94×	body	1280	valid
18.0ms	50×	body	640	valid
9.0ms	44×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	11×	body	80	valid

simplify420.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 31.1b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (sin x))
1.3b	(- x (tan x))

rewrite19.0ms

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

series37.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (sin x))
20.0ms	(- x (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5236	1127

prune107.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	6	88

Merged error: 0.0b

Counts

88 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.9b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite42.0ms

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 → 91

Calls

4 calls:

6.0ms	(/ (sin x) (- x (tan x)))
27.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series62.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (sin x) (- x (tan x)))
29.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
9.0ms	(- x (tan x))
10.0ms	(- x (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4948	1408
1	4948	1408

prune96.0ms

Filtered

80 candidates to 103 candidates (-28.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	103	6	109

Merged error: 0.0b

Counts

109 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
1.3b	(- x (sin x))
1.3b	(- x (tan x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
62×	`unpow-prod-down` `cube-prod`
50×	`add-cube-cbrt`
42×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 186

Calls

4 calls:

10.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
11.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
5.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series49.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
13.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
4.0ms	(- x (sin x))
10.0ms	(- x (tan x))

simplify59.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5245	3340

prune146.0ms

Filtered

87 candidates to 198 candidates (-127.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	197	7	204

Merged error: 0b

Counts

204 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

1.3b	(- x (sin x))
1.3b	(- x (tan x))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite14.0ms

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- x (sin x))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))
12.0ms	(- x (tan x))

simplify36.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5345	510

prune66.0ms

Filtered

51 candidates to 64 candidates (-25.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	64	7	71

Merged error: 0b

Counts

71 → 7

regimes102.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch53.0ms

Steps

Iters	Range		Point
9	1.7298563504608262e-06	22.03225909356051	0.03592679795301445
8	-9.448423108950664	-0.002904522370188349	-0.028107423104785232

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	47
1	32	47

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

sample6.7s

Algorithm

intervals

Results

4.2s	1625×	body	2560	valid
1.7s	2745×	body	1280	valid
484.0ms	1867×	body	640	valid
170.0ms	980×	body	320	valid
59.0ms	476×	body	160	valid
27.0ms	307×	body	80	valid

Details

analyze1.3s

sample230.0ms

simplify420.0ms

prune4.0ms

localize11.0ms

rewrite19.0ms

series37.0ms

simplify46.0ms

prune107.0ms

localize10.0ms

rewrite42.0ms

series62.0ms

simplify52.0ms

prune96.0ms

localize11.0ms

rewrite38.0ms

series49.0ms

simplify59.0ms

prune146.0ms

localize14.0ms

rewrite14.0ms

series36.0ms

simplify36.0ms

prune66.0ms

regimes102.0ms

bsearch53.0ms

simplify2.0ms

end0.0ms

analyze1.1s

sample6.7s

Profiling