Details

analyze2.0ms (0%)

Algorithm

1×

Search

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

sample95.0ms (2.1%)

Algorithm

1×

intervals

Results

49.0ms	136×	body	1280	valid
17.0ms	19×	body	2560	valid
15.0ms	65×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune11.0ms (0.2%)

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: 40.2b

Counts

2 → 1

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.6b	(- (cos (+ x eps)) (cos x))
3.3b	(cos (+ x eps))

rewrite10.0ms (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))

series14.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

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

simplify24.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4999	270
1	4999	270

prune66.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	22	7	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	7	30

Merged error: 0.4b

Counts

30 → 7

localize13.0ms (0.3%)

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))

rewrite34.0ms (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))

series38.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
14.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
6.0ms	(sin (/ (+ x (+ x eps)) 2))
4.0ms	(+ x (+ x eps))

simplify54.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4907	890
1	4907	890

prune188.0ms (4.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	63	9	72
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	66	13	79

Merged error: 0.4b

Counts

79 → 13

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
3.3b	(sin (/ (+ x (+ x eps)) 2))
3.3b	(sin (/ (+ x (+ x eps)) 2))
3.3b	(sin (/ (+ x (+ x eps)) 2))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

8.0ms	(sin (/ (+ x (+ x eps)) 2))
7.0ms	(sin (/ (+ x (+ x eps)) 2))
7.0ms	(sin (/ (+ x (+ x eps)) 2))
6.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))

series37.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))
6.0ms	(sin (/ (+ x (+ x eps)) 2))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify47.0ms (1%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5090	468

prune192.0ms (4.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	44	13	57

Merged error: 0.4b

Counts

57 → 13

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
3.3b	(sin (/ (+ x (+ x eps)) 2))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

8.0ms	(sin (/ (+ x (+ x eps)) 2))
2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))

series60.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (sin (/ eps 2)))
18.0ms	(cbrt (sin (/ eps 2)))
18.0ms	(cbrt (sin (/ eps 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5501	442

prune171.0ms (3.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	51	14	65

Merged error: 0.4b

Counts

65 → 14

regimes227.0ms (5%)

Accuracy

Total 0.4b remaining (52%)

Threshold costs 0.4b (52%)

bsearch63.0ms (1.4%)

Steps

Iters	Range		Point
9	0.17949788472177558	45623308.59113779	0.18290653919849093
7	-9.494300489779706e-09	-4.726833690786262e-10	-9.370340767231984e-09

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	38
1	78	38

end0.0ms (0%)

sample3.1s (67.5%)

Algorithm

1×

intervals

Results

1.7s	4510×	body	1280	valid
588.0ms	631×	body	2560	valid
420.0ms	1814×	body	640	valid
106.0ms	660×	body	320	valid
34.0ms	299×	body	160	valid
10.0ms	86×	body	80	valid

Details

analyze2.0ms (0%)

sample95.0ms (2.1%)

simplify4.0ms (0.1%)

prune11.0ms (0.2%)

localize9.0ms (0.2%)

rewrite10.0ms (0.2%)

series14.0ms (0.3%)

simplify24.0ms (0.5%)

prune66.0ms (1.5%)

localize13.0ms (0.3%)

rewrite34.0ms (0.8%)

series38.0ms (0.8%)

simplify54.0ms (1.2%)

prune188.0ms (4.2%)

localize17.0ms (0.4%)

rewrite28.0ms (0.6%)

series37.0ms (0.8%)

simplify47.0ms (1%)

prune192.0ms (4.2%)

localize17.0ms (0.4%)

rewrite15.0ms (0.3%)

series60.0ms (1.3%)

simplify30.0ms (0.7%)

prune171.0ms (3.8%)

regimes227.0ms (5%)

bsearch63.0ms (1.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.1s (67.5%)

Profiling