Details

analyze2.0ms

Algorithm

Search

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

sample100.0ms

Algorithm

intervals

Results

51.0ms	137×	body	1280	valid
16.0ms	18×	body	2560	valid
13.0ms	60×	body	640	valid
11.0ms	30×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	7
1	7	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: 39.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ x eps))

rewrite10.0ms

Algorithm

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

Counts

2 → 6

Calls

2 calls:

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

simplify62.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4816	270
1	4816	270

prune64.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	21	8	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	8	30

Merged error: 0.3b

Counts

30 → 8

localize13.0ms

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)))
3.8b	(sin (/ (+ x (+ x eps)) 2))

rewrite37.0ms

Algorithm

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))))
5.0ms	(+ x (+ x eps))
13.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms	(sin (/ (+ x (+ x eps)) 2))

series36.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
4.0ms	(+ x (+ x eps))
12.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify60.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4847	891
1	4847	891

prune151.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	65	7	72
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	68	12	80

Merged error: 0.3b

Counts

80 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
3.8b	(sin (/ (+ x (+ x eps)) 2))
3.8b	(sin (/ (+ x (+ x eps)) 2))
3.8b	(sin (/ (+ x (+ x eps)) 2))

rewrite26.0ms

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:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(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))

simplify58.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4907	469
1	4907	469

prune154.0ms

Filtered

38 candidates to 44 candidates (-15.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	44	12	56

Merged error: 0.3b

Counts

56 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3)))
0.6b	(pow (sin (/ (+ x (+ x eps)) 2)) 3)
3.8b	(sin (/ (+ x (+ x eps)) 2))
6.1b	(cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 85

Calls

4 calls:

13.0ms	(* (sin (/ eps 2)) (cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3)))
7.0ms	(pow (sin (/ (+ x (+ x eps)) 2)) 3)
7.0ms	(sin (/ (+ x (+ x eps)) 2))
9.0ms	(cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3))

series38.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (sin (/ eps 2)) (cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3)))
15.0ms	(pow (sin (/ (+ x (+ x eps)) 2)) 3)
6.0ms	(sin (/ (+ x (+ x eps)) 2))
6.0ms	(cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3))

simplify60.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4937	1267
1	4937	1267

prune130.0ms

Filtered

55 candidates to 97 candidates (-76.4%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	96	13	109

Merged error: 0.3b

Counts

109 → 13

regimes207.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 15.0b

bsearch113.0ms

Steps

Iters	Range		Point
9	6.581657935485426e-10	0.0007933650446723445	9.533176048648487e-06
10	-0.2907404391033222	-1.9224311918263173e-14	-1.2823417273874109e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	38
1	35	38

end0.0ms

analyze1.0ms

Algorithm

Search

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

sample3.0s

Algorithm

intervals

Results

1.6s	4407×	body	1280	valid
608.0ms	672×	body	2560	valid
421.0ms	1865×	body	640	valid
108.0ms	699×	body	320	valid
35.0ms	283×	body	160	valid
4.0ms	74×	body	80	valid

Details

analyze2.0ms

sample100.0ms

simplify3.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series14.0ms

simplify62.0ms

prune64.0ms

localize13.0ms

rewrite37.0ms

series36.0ms

simplify60.0ms

prune151.0ms

localize17.0ms

rewrite26.0ms

series40.0ms

simplify58.0ms

prune154.0ms

localize15.0ms

rewrite38.0ms

series38.0ms

simplify60.0ms

prune130.0ms

regimes207.0ms

bsearch113.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample3.0s

Profiling