Details

analyze2.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 100%

sample105.0ms

Algorithm

intervals

Results

51.0ms	116×	body	1280	valid
20.0ms	22×	body	2560	valid
19.0ms	58×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	32×	body	80	valid
1.0ms	10×	body	160	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: 36.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (sin (+ x eps)) (sin x))
2.6b	(sin (+ 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` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

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))

simplify135.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	133	175
1	301	165
2	937	164
3	3445	164
4	5001	164

prune61.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 13.2b

Counts

31 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
2.1b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`sin-cos-mult`
2×	`sub-neg` `associate-+r+` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* (cos x) (sin eps)) (sin x))
4.0ms	(* (cos x) (sin eps))
4.0ms	(* (sin x) (cos eps))
8.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (* (cos x) (sin eps)) (sin x))
9.0ms	(* (cos x) (sin eps))
8.0ms	(* (sin x) (cos eps))
21.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	348	614
1	1352	580
2	5002	565

prune124.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	67	11	78
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	74	11	85

Merged error: 0.2b

Counts

85 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (- (cos eps) 1))
0.1b	(* (cos x) (sin eps))
0.2b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
1.4b	(- (cos eps) 1)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-r`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `difference-of-squares`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

7.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(* (cos x) (sin eps))
8.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
4.0ms	(- (cos eps) 1)

series42.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin x) (- (cos eps) 1))
9.0ms	(* (cos x) (sin eps))
21.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
3.0ms	(- (cos eps) 1)

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	337	546
1	1279	498
2	5001	497

prune140.0ms

Filtered

56 candidates to 89 candidates (-58.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	87	13	100

Merged error: 0.1b

Counts

100 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
0.2b	(+ (+ (* (sin x) (cos eps)) (* -1 (sin x))) (* (cos x) (sin eps)))
1.5b	(+ (* (sin x) (cos eps)) (* -1 (sin x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`mul-1-neg` `sum-log`
2×	`+-commutative` `associate-+l-` `flip3-+` `unsub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`associate-+l+` `sin-cos-mult`

Counts

4 → 65

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
4.0ms	(* (sin x) (cos eps))
8.0ms	(+ (+ (* (sin x) (cos eps)) (* -1 (sin x))) (* (cos x) (sin eps)))
5.0ms	(+ (* (sin x) (cos eps)) (* -1 (sin x)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos x) (sin eps))
9.0ms	(* (sin x) (cos eps))
23.0ms	(+ (+ (* (sin x) (cos eps)) (* -1 (sin x))) (* (cos x) (sin eps)))
11.0ms	(+ (* (sin x) (cos eps)) (* -1 (sin x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	336	562
1	1358	507
2	5002	494

prune74.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	77	13	90

Merged error: 0.1b

Counts

90 → 13

regimes171.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

analyze2.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 100%

sample3.1s

Algorithm

intervals

Results

1.5s	3290×	body	1280	valid
653.0ms	674×	body	2560	valid
518.0ms	1852×	body	640	valid
138.0ms	760×	body	320	valid
62.0ms	1073×	body	80	valid
48.0ms	351×	body	160	valid

Details

analyze2.0ms

sample105.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series13.0ms

simplify135.0ms

prune61.0ms

localize17.0ms

rewrite23.0ms

series50.0ms

simplify42.0ms

prune124.0ms

localize17.0ms

rewrite25.0ms

series42.0ms

simplify43.0ms

prune140.0ms

localize15.0ms

rewrite22.0ms

series52.0ms

simplify44.0ms

prune74.0ms

regimes171.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.0ms

sample3.1s

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