Details

sample100.0ms

Algorithm

intervals

Results

48.0ms	109×	body	1280	valid
18.0ms	20×	body	2560	valid
17.0ms	68×	body	640	valid
5.0ms	27×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	21×	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: 38.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
3.5b	(sin (+ x eps))

rewrite12.0ms

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))

series65.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (sin (+ x eps)) (sin x))
25.0ms	(sin (+ x eps))

simplify139.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	133	175
1	301	166
2	937	164
3	3445	164
4	5001	164

prune80.0ms

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: 15.2b

Counts

31 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(- (* (cos x) (sin eps)) (sin x))
0.2b	(* (sin x) (cos eps))
3.4b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite24.0ms

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

series268.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos x) (sin eps))
59.0ms	(- (* (cos x) (sin eps)) (sin x))
48.0ms	(* (sin x) (cos eps))
112.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	348	614
1	1352	581
2	5002	565

prune210.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	68	10	78
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	77	10	87

Merged error: 0.5b

Counts

87 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.2b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (- (cos eps) 1))
1.8b	(- (cos eps) 1)

rewrite28.0ms

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:

5.0ms	(* (cos x) (sin eps))
9.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
8.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(- (cos eps) 1)

series225.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos x) (sin eps))
110.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
45.0ms	(* (sin x) (- (cos eps) 1))
23.0ms	(- (cos eps) 1)

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	333	552
1	1271	503
2	5002	501

prune216.0ms

Filtered

89 candidates to 57 candidates (64.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	87	12	99

Merged error: 0.1b

Counts

99 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1)))
0.2b	(/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1))
0.3b	(* (sin eps) (sin eps))
0.5b	(+ (cos eps) 1)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
49×	`times-frac`
39×	`add-sqr-sqrt`
33×	`associate-r`
32×	`add-cube-cbrt`
14×	`distribute-lft-out`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
6×	`associate-l` `associate-/l*` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `swap-sqr` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `distribute-frac-neg` `div-exp` `pow-prod-down` `*-commutative` `div-inv` `sin-mult`
1×	`+-commutative` `pow2` `neg-sub0` `frac-2neg` `pow-plus` `div-sub` `associate-*r/` `clear-num` `sum-log` `pow-sqr` `pow-prod-up` `distribute-rgt-neg-out` `sqr-sin` `associate-/l/` `distribute-neg-frac`

Counts

4 → 140

Calls

4 calls:

13.0ms	(* (sin x) (/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1)))
7.0ms	(/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1))
5.0ms	(* (sin eps) (sin eps))
4.0ms	(+ (cos eps) 1)

series194.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (sin x) (/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1)))
60.0ms	(/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1))
18.0ms	(* (sin eps) (sin eps))
11.0ms	(+ (cos eps) 1)

simplify105.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	512	1250
1	2976	1104
2	5001	1096

prune385.0ms

Filtered

152 candidates to 111 candidates (73.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	152	12	164

Merged error: 0.1b

Counts

164 → 12

regimes105.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	27	11
2	31	11
3	31	11

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	3365×	body	1280	valid
589.0ms	637×	body	2560	valid
475.0ms	1815×	body	640	valid
147.0ms	770×	body	320	valid
58.0ms	1080×	body	80	valid
38.0ms	333×	body	160	valid