Details

sample95.0ms

Algorithm

intervals

Results

56.0ms	151×	body	1280	valid
12.0ms	54×	body	640	valid
12.0ms	14×	body	2560	valid
3.0ms	23×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	2×	body	80	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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 38.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (cos (+ x eps)) (cos x))
2.8b	(cos (+ 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` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

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

series71.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify111.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune78.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	21	9	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	9	31

Merged error: 14.3b

Counts

31 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.3b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite24.0ms

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`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series303.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos x) (cos eps))
85.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
129.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify113.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4487	583
3	5002	583

prune225.0ms

Filtered

82 candidates to 57 candidates (69.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	68	14	82
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	73	18	91

Merged error: 14.2b

Counts

91 → 18

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.3b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite28.0ms

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×	`cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `sin-mult` `associate--r+`

Counts

4 → 65

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
6.0ms	(+ (* (sin x) (sin eps)) (cos x))
5.0ms	(* (sin x) (sin eps))
13.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (cos eps))
49.0ms	(+ (* (sin x) (sin eps)) (cos x))
49.0ms	(* (sin x) (sin eps))
126.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	576
2	5002	567

prune221.0ms

Filtered

77 candidates to 53 candidates (68.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	6	11	17
Picked	1	0	1
Done	0	0	0
Total	75	20	95

Merged error: 14.2b

Counts

95 → 20

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
2.3b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
27.5b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`cbrt-prod` `add-cube-cbrt`
3×	`pow-unpow` `diff-log` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `sub-neg` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `associate--l+` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `cbrt-div` `flip3--` `pow1/3` `*-commutative` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

9.0ms	(* (sin x) (sin eps))
5.0ms	(pow (* (sin x) (sin eps)) 3)
10.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
3.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series292.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin x) (sin eps))
63.0ms	(pow (* (sin x) (sin eps)) 3)
135.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
44.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	293	634
1	1142	580
2	5001	565

prune203.0ms

Filtered

90 candidates to 60 candidates (66.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	18	19
Picked	0	1	1
Done	0	0	0
Total	90	20	110

Merged error: 14.1b

Counts

110 → 20

regimes199.0ms

Accuracy

83.3% (1.6b remaining)

Error of 16.3b against oracle of 14.7b and baseline of 24.5b

bsearch109.0ms

Steps

Iters	Range		Point
8	1.3803315812694795e-08	1.8094954886202674e-05	1.6985852405271936e-07
8	-1.2056568586554778e-13	-1.4903061489544405e-16	-1.184078211908822e-13

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	38
1	38	38

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.8s	4486×	body	1280	valid
551.0ms	634×	body	2560	valid
408.0ms	1841×	body	640	valid
105.0ms	671×	body	320	valid
32.0ms	299×	body	160	valid
4.0ms	69×	body	80	valid