Details

analyze816.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample98.0ms

Algorithm

intervals

Results

47.0ms	116×	body	1280	valid
18.0ms	20×	body	2560	valid
18.0ms	49×	body	640	valid
3.0ms	22×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	29×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune3.0ms

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: 38.0b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (tan (+ x eps)) (tan x))
3.0b	(tan (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

7.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series39.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- (tan (+ x eps)) (tan x))
15.0ms	(tan (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (21.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune64.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	22	9	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	9	32

Merged error: 16.5b

Counts

32 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series194.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
20.0ms	(+ (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
96.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	994

prune177.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	82	16	98
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	89	18	107

Merged error: 16.3b

Counts

107 → 18

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.1b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
3.4b	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`tan-quot`
19×	`*-un-lft-identity`
18×	`associate-r`
15×	`add-exp-log`
14×	`add-cube-cbrt`
11×	`times-frac` `add-cbrt-cube`
8×	`pow1` `frac-sub` `add-log-exp`
7×	`frac-times` `associate-l` `associate-*l/`
5×	`flip3-+` `frac-add` `prod-exp` `flip-+`
4×	`unswap-sqr`
3×	`associate-*r/` `cbrt-unprod`
2×	`flip3--` `div-exp` `pow-prod-down` `associate-/r/` `un-div-inv` `*-commutative` `flip--` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rec-exp` `diff-log` `1-exp` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

12.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series261.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
24.0ms	(+ (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
153.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify69.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	561	1286
1	2547	1185
2	5001	1184

prune206.0ms

Filtered

83 candidates to 111 candidates (-33.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	1	16	17
Picked	1	0	1
Done	0	0	0
Total	109	20	129

Merged error: 16.2b

Counts

129 → 20

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
0.2b	(* (sin x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
5×	`tan-quot`
4×	`times-frac`
3×	`associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `clear-num` `sum-log` `-commutative` `frac-sub` `flip--` `flip-+` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
5.0ms	(/ (* (sin x) (tan eps)) (cos x))
5.0ms	(* (sin x) (tan eps))
19.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series159.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan x) (tan eps))
23.0ms	(/ (* (sin x) (tan eps)) (cos x))
18.0ms	(* (sin x) (tan eps))
98.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	389	785
1	1406	711
2	5001	699

prune79.0ms

Filtered

60 candidates to 82 candidates (-36.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	19	19
Picked	1	0	1
Done	0	0	0
Total	82	20	102

Merged error: 16.2b

Counts

102 → 20

regimes238.0ms

Accuracy

86% (1.0b remaining)

Error of 15.6b against oracle of 14.6b and baseline of 22.0b

bsearch221.0ms

Steps

Iters	Range		Point
8	1.0838620297170299e-93	1.2531557249088682e-89	1.2324991421784307e-89
8	-1.8939158318385254e-16	-3.884758653989066e-19	-6.412434821960689e-18

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	18
1	38	18

end0.0ms

analyze761.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample2.7s

Algorithm

intervals

Results

1.4s	3372×	body	1280	valid
565.0ms	632×	body	2560	valid
406.0ms	1782×	body	640	valid
116.0ms	762×	body	320	valid
50.0ms	1122×	body	80	valid
35.0ms	330×	body	160	valid

Details

analyze816.0ms

sample98.0ms

simplify4.0ms

prune3.0ms

localize9.0ms

rewrite11.0ms

series39.0ms

simplify75.0ms

prune64.0ms

localize14.0ms

rewrite30.0ms

series194.0ms

simplify48.0ms

prune177.0ms

localize12.0ms

rewrite35.0ms

series261.0ms

simplify69.0ms

prune206.0ms

localize18.0ms

rewrite36.0ms

series159.0ms

simplify48.0ms

prune79.0ms

regimes238.0ms

bsearch221.0ms

simplify1.0ms

end0.0ms

analyze761.0ms

sample2.7s

Profiling