Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample106.0ms (2.4%)

Algorithm

1×

intervals

Results

52.0ms	140×	body	1280	valid
27.0ms	24×	body	2560	valid
13.0ms	59×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune6.0ms (0.1%)

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: 41.0b

Counts

2 → 1

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
3.4b	(cos (+ x eps))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 23

Calls

2 calls:

6.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series15.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

simplify27.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4999	270
1	4999	270

prune63.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	23	6	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	6	30

Merged error: 0.3b

Counts

30 → 6

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
3.3b	(sin (/ (+ x (+ x eps)) 2))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

11.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
10.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms	(sin (/ (+ x (+ x eps)) 2))
5.0ms	(+ x (+ x eps))

series36.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
11.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms	(sin (/ (+ x (+ x eps)) 2))
4.0ms	(+ x (+ x eps))

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4907	890
1	4907	890

prune180.0ms (4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	67	11	78

Merged error: 0.3b

Counts

78 → 11

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (+ x (* eps 1/2)))))
0.3b	(* (sin (/ eps 2)) (sin (+ x (* eps 1/2))))
3.4b	(sin (+ x (* eps 1/2)))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`sin-sum`
6×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 52

Calls

3 calls:

8.0ms	(* -2 (* (sin (/ eps 2)) (sin (+ x (* eps 1/2)))))
8.0ms	(* (sin (/ eps 2)) (sin (+ x (* eps 1/2))))
4.0ms	(sin (+ x (* eps 1/2)))

series30.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

13.0ms	(* -2 (* (sin (/ eps 2)) (sin (+ x (* eps 1/2)))))
11.0ms	(* (sin (/ eps 2)) (sin (+ x (* eps 1/2))))
5.0ms	(sin (+ x (* eps 1/2)))

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4816	851
1	4816	851

prune171.0ms (3.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	54	7	61
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 0.1b

Counts

72 → 12

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
0.1b	(* (sin x) (cos (* eps 1/2)))
0.2b	(* (cos x) (sin (* eps 1/2)))
0.3b	(* (sin (/ eps 2)) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `associate-*r/` `flip-+`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `sum-log` `sin-cos-mult`

Counts

4 → 70

Calls

4 calls:

10.0ms	(* (sin (/ eps 2)) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
7.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
5.0ms	(* (cos x) (sin (* eps 1/2)))
5.0ms	(* (sin x) (cos (* eps 1/2)))

series62.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (sin (/ eps 2)) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
18.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
9.0ms	(* (cos x) (sin (* eps 1/2)))
9.0ms	(* (sin x) (cos (* eps 1/2)))

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5030	1237

prune204.0ms (4.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	79	15	94

Merged error: 0.0b

Counts

94 → 15

regimes215.0ms (4.8%)

Accuracy

Total 0.3b remaining (88.3%)

Threshold costs 0.3b (88.3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	27
1	25	27

end0.0ms (0%)

sample3.0s (67.4%)

Algorithm

1×

intervals

Results

1.7s	4439×	body	1280	valid
590.0ms	646×	body	2560	valid
454.0ms	1872×	body	640	valid
108.0ms	678×	body	320	valid
32.0ms	288×	body	160	valid
9.0ms	77×	body	80	valid

Details

analyze2.0ms (0%)

sample106.0ms (2.4%)

simplify5.0ms (0.1%)

prune6.0ms (0.1%)

localize8.0ms (0.2%)

rewrite11.0ms (0.2%)

series15.0ms (0.3%)

simplify27.0ms (0.6%)

prune63.0ms (1.4%)

localize16.0ms (0.4%)

rewrite35.0ms (0.8%)

series36.0ms (0.8%)

simplify57.0ms (1.3%)

prune180.0ms (4%)

localize12.0ms (0.3%)

rewrite22.0ms (0.5%)

series30.0ms (0.7%)

simplify76.0ms (1.7%)

prune171.0ms (3.8%)

localize23.0ms (0.5%)

rewrite28.0ms (0.6%)

series62.0ms (1.4%)

simplify56.0ms (1.2%)

prune204.0ms (4.6%)

regimes215.0ms (4.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample3.0s (67.4%)

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