Details

sample97.0ms

Algorithm

intervals

Results

40.0ms	94×	body	1280	valid
22.0ms	25×	body	2560	valid
17.0ms	67×	body	640	valid
5.0ms	30×	body	320	valid
2.0ms	30×	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

localize14.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (sin (+ x eps)) (sin x))
1.9b	(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))

series58.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify140.0ms

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

prune82.0ms

Filtered

30 candidates to 23 candidates (76.7%)

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: 16.0b

Counts

31 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
2.8b	(- (+ (* (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:

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

series292.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
43.0ms	(* (cos x) (sin eps))
48.0ms	(* (sin x) (cos eps))
112.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify42.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

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

prune203.0ms

Filtered

76 candidates to 54 candidates (71.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	76	8	84

Merged error: 0.3b

Counts

84 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (- (cos eps) 1))
0.2b	(* (cos x) (sin eps))
1.9b	(- (cos eps) 1)

rewrite32.0ms

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)))
12.0ms	(* (sin x) (- (cos eps) 1))
5.0ms	(* (cos x) (sin eps))
4.0ms	(- (cos eps) 1)

series225.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
51.0ms	(* (sin x) (- (cos eps) 1))
43.0ms	(* (cos x) (sin eps))
20.0ms	(- (cos eps) 1)

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5001	499

prune227.0ms

Filtered

89 candidates to 56 candidates (62.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	84	13	97

Merged error: 0.0b

Counts

97 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (cos eps) 3) 1) (+ (* (cos eps) (+ (cos eps) 1)) 1))
0.4b	(pow (cos eps) 3)
0.4b	(+ (cos eps) 1)
1.7b	(- (pow (cos eps) 3) 1)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
48×	`times-frac`
40×	`difference-of-squares`
28×	`add-cube-cbrt`
20×	`difference-of-sqr-1`
18×	`unpow-prod-down` `cube-prod`
16×	`associate-/l*` `sqr-pow`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out--`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 144

Calls

4 calls:

17.0ms	(/ (- (pow (cos eps) 3) 1) (+ (* (cos eps) (+ (cos eps) 1)) 1))
3.0ms	(pow (cos eps) 3)
4.0ms	(+ (cos eps) 1)
7.0ms	(- (pow (cos eps) 3) 1)

series393.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- (pow (cos eps) 3) 1) (+ (* (cos eps) (+ (cos eps) 1)) 1))
28.0ms	(pow (cos eps) 3)
9.0ms	(+ (cos eps) 1)
254.0ms	(- (pow (cos eps) 3) 1)

simplify97.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	485	1779
1	2276	1691
2	5002	1632

prune314.0ms

Filtered

156 candidates to 78 candidates (50.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	155	14	169

Merged error: 0.0b

Counts

169 → 14

regimes121.0ms

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	27	17
1	27	17

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	3279×	body	1280	valid
580.0ms	623×	body	2560	valid
495.0ms	1876×	body	640	valid
138.0ms	778×	body	320	valid
61.0ms	1091×	body	80	valid
40.0ms	353×	body	160	valid