Details

analyze1.0ms

Algorithm

Search

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

sample103.0ms

Algorithm

intervals

Results

47.0ms	105×	body	1280	valid
19.0ms	21×	body	2560	valid
16.0ms	62×	body	640	valid
6.0ms	32×	body	80	valid
4.0ms	25×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

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: 37.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
2.7b	(sin (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 23

Calls

2 calls:

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

series13.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

simplify44.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5348	268

prune49.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.3b

Counts

30 → 3

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
2.6b	(cos (/ (+ x (+ x eps)) 2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

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

series21.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (+ x eps))
11.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5169	541

prune115.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	45	8	53

Merged error: 0.3b

Counts

53 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ x (+ x eps)) 2)))
2.6b	(cos (/ (+ x (+ x eps)) 2))
2.6b	(cos (/ (+ x (+ x eps)) 2))
2.6b	(cos (/ (+ x (+ x eps)) 2))

rewrite23.0ms

Algorithm

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:

1.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
7.0ms	(cos (/ (+ x (+ x eps)) 2))
7.0ms	(cos (/ (+ x (+ x eps)) 2))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series35.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
6.0ms	(cos (/ (+ x (+ x eps)) 2))
5.0ms	(cos (/ (+ x (+ x eps)) 2))
6.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify70.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4872	415
1	4872	415

prune166.0ms

Filtered

37 candidates to 44 candidates (-18.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	43	9	52

Merged error: 0.2b

Counts

52 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
2.6b	(cos (/ (+ x (+ x eps)) 2))
2.6b	(cos (/ (+ x (+ x eps)) 2))
2.6b	(cos (/ (+ x (+ x eps)) 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 30

Calls

4 calls:

3.0ms	(cbrt (* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
7.0ms	(cos (/ (+ x (+ x eps)) 2))
7.0ms	(cos (/ (+ x (+ x eps)) 2))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series47.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt (* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
5.0ms	(cos (/ (+ x (+ x eps)) 2))
5.0ms	(cos (/ (+ x (+ x eps)) 2))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify48.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5157	465

prune160.0ms

Filtered

37 candidates to 42 candidates (-13.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	42	9	51

Merged error: 0.2b

Counts

51 → 9

regimes179.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.0b

bsearch79.0ms

Steps

Iters	Range		Point
10	4.3922265410796777e-17	6.615862107880164	1.1421815710415283e-08
9	-4.5309087082570456e-08	-1.6657409484079213e-16	-1.1753520811402347e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	51
1	47	51

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	3289×	body	1280	valid
636.0ms	675×	body	2560	valid
497.0ms	1811×	body	640	valid
143.0ms	760×	body	320	valid
68.0ms	1132×	body	80	valid
44.0ms	333×	body	160	valid

Details

analyze1.0ms

sample103.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite11.0ms

series13.0ms

simplify44.0ms

prune49.0ms

localize13.0ms

rewrite19.0ms

series21.0ms

simplify57.0ms

prune115.0ms

localize19.0ms

rewrite23.0ms

series35.0ms

simplify70.0ms

prune166.0ms

localize18.0ms

rewrite26.0ms

series47.0ms

simplify48.0ms

prune160.0ms

regimes179.0ms

bsearch79.0ms

simplify1.0ms

end0.0ms

sample3.0s

Profiling