Details

sample90.0ms

Algorithm

intervals

Results

45.0ms	107×	body	1280	valid
16.0ms	18×	body	2560	valid
12.0ms	51×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	10×	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

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: 36.3b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (sin (+ x eps)) (sin x))
3.6b	(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))

series55.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify139.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

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

prune81.0ms

Filtered

30 candidates to 23 candidates (76.7%)

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: 14.6b

Counts

31 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (cos eps))
3.7b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin 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`
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:

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

series277.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (sin eps))
85.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
44.0ms	(* (sin x) (cos eps))
107.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	308	589
1	1168	555
2	5001	543

prune221.0ms

Filtered

76 candidates to 54 candidates (71.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 0.3b

Counts

83 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (- (cos eps) 1))
1.7b	(- (cos eps) 1)

rewrite26.0ms

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:

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

series220.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos x) (sin eps))
108.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
43.0ms	(* (sin x) (- (cos eps) 1))
22.0ms	(- (cos eps) 1)

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

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

prune228.0ms

Filtered

89 candidates to 56 candidates (62.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	7	2	9
Picked	0	1	1
Done	0	0	0
Total	89	10	99

Merged error: 0.0b

Counts

99 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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:

7.0ms	(/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1))
16.0ms	(* (sin x) (/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1)))
5.0ms	(* (sin eps) (sin eps))
4.0ms	(+ (cos eps) 1)

series190.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1))
104.0ms	(* (sin x) (/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1)))
19.0ms	(* (sin eps) (sin eps))
10.0ms	(+ (cos eps) 1)

simplify106.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (94.0ms)

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

prune455.0ms

Filtered

152 candidates to 110 candidates (72.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	152	10	162

Merged error: 0.0b

Counts

162 → 10

regimes88.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	29	13
2	32	13
3	32	13

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	3322×	body	1280	valid
581.0ms	635×	body	2560	valid
484.0ms	1830×	body	640	valid
135.0ms	767×	body	320	valid
66.0ms	1102×	body	80	valid
40.0ms	344×	body	160	valid