Details

sample104.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

42.0ms	93×	body	1280	valid
23.0ms	23×	body	2560	valid
16.0ms	58×	body	640	valid
5.0ms	26×	body	320	valid
2.0ms	41×	body	80	valid
2.0ms	15×	body	160	valid

simplify5.0ms

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: 37.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
3.4b	(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 → 24

Calls

2 calls:

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(- (sin (+ x eps)) (sin x))
6.0ms	(sin (+ x eps))

simplify142.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

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

prune66.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 15.2b

Counts

31 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
3.3b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

5.0ms	(* (sin x) (cos eps))
6.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
8.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series60.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin x) (cos eps))
18.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
9.0ms	(* (cos x) (sin eps))
23.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify44.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	308	589
1	1168	554
2	5001	543

prune107.0ms

Filtered

53 candidates to 76 candidates (-43.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	74	10	84

Merged error: 0.1b

Counts

84 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (- (cos eps) 1))
1.0b	(- (cos eps) 1)

rewrite27.0ms

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:

9.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
8.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(- (cos eps) 1)

series42.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
9.0ms	(* (cos x) (sin eps))
9.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(- (cos eps) 1)

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	337	546
1	1279	498
2	5002	497

prune128.0ms

Filtered

55 candidates to 89 candidates (-61.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	78	11	89
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	86	13	99

Merged error: 0.1b

Counts

99 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (* (sin x) (cos eps)) (* -1 (sin x))) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))
0.1b	(* (cos x) (sin eps))
1.0b	(+ (* (sin x) (cos eps)) (* -1 (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`
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:

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

series52.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify45.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (39.0ms)

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	73	4	77
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	77	13	90

Merged error: 0.1b

Counts

90 → 13

regimes163.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	15
1	20	15

end0.0ms

sample3.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

1.6s	3306×	body	1280	valid
656.0ms	657×	body	2560	valid
493.0ms	1816×	body	640	valid
143.0ms	752×	body	320	valid
67.0ms	1134×	body	80	valid
47.0ms	335×	body	160	valid

Details

sample104.0ms

simplify5.0ms

prune3.0ms

localize9.0ms

rewrite11.0ms

series14.0ms

simplify142.0ms

prune66.0ms

localize14.0ms

rewrite25.0ms

series60.0ms

simplify44.0ms

prune107.0ms

localize17.0ms

rewrite27.0ms

series42.0ms

simplify47.0ms

prune128.0ms

localize15.0ms

rewrite23.0ms

series52.0ms

simplify45.0ms

prune74.0ms

regimes163.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Profiling