Details

sample95.0ms

Algorithm

intervals

Results

47.0ms	111×	body	1280	valid
17.0ms	19×	body	2560	valid
13.0ms	52×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	20×	body	160	valid
2.0ms	29×	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: 39.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (sin (+ x eps)) (sin x))
5.0b	(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))

series62.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
17.0ms	(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

prune85.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	24	6	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	6	31

Merged error: 14.4b

Counts

31 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
3.7b	(+ (* (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	(* (sin x) (cos eps))
4.0ms	(- (* (cos x) (sin eps)) (sin x))
4.0ms	(* (cos x) (sin eps))
9.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin x) (cos eps))
64.0ms	(- (* (cos x) (sin eps)) (sin x))
43.0ms	(* (cos x) (sin eps))
116.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (37.0ms)

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

prune252.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	66	12	78
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	72	12	84

Merged error: 0.6b

Counts

84 → 12

localize15.0ms

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))
2.9b	(- (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:

9.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
7.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(- (cos eps) 1)

series228.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
48.0ms	(* (cos x) (sin eps))
49.0ms	(* (sin x) (- (cos eps) 1))
19.0ms	(- (cos eps) 1)

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

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

prune248.0ms

Filtered

89 candidates to 56 candidates (62.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	88	13	101

Merged error: 0.1b

Counts

101 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (cos eps) 1))
0.2b	(* (sin x) (log (exp (- (cos eps) 1))))
2.9b	(- (cos eps) 1)
2.9b	(log (exp (- (cos eps) 1)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
21×	`exp-prod`
16×	`log-pow`
15×	`log-prod`
12×	`add-cube-cbrt`
11×	`associate-r`
9×	`add-log-exp`
8×	`pow1` `exp-sum` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
4×	`difference-of-sqr-1` `distribute-lft-out--`
3×	`associate-l`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`log-div` `flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

5.0ms	(exp (- (cos eps) 1))
14.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
4.0ms	(- (cos eps) 1)
5.0ms	(log (exp (- (cos eps) 1)))

series129.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(exp (- (cos eps) 1))
51.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
18.0ms	(- (cos eps) 1)
20.0ms	(log (exp (- (cos eps) 1)))

simplify113.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	224	572
1	814	478
2	3441	467
3	5002	467

prune268.0ms

Filtered

105 candidates to 68 candidates (64.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	104	14	118

Merged error: 0.1b

Counts

118 → 14

regimes131.0ms

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	18	10
1	18	10

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	3343×	body	1280	valid
556.0ms	613×	body	2560	valid
479.0ms	1785×	body	640	valid
138.0ms	733×	body	320	valid
70.0ms	1153×	body	80	valid
43.0ms	373×	body	160	valid

Details

sample95.0ms

simplify5.0ms

prune2.0ms

localize9.0ms

rewrite11.0ms

series62.0ms

simplify140.0ms

prune85.0ms

localize15.0ms

rewrite24.0ms

series265.0ms

simplify44.0ms

prune252.0ms

localize15.0ms

rewrite26.0ms

series228.0ms

simplify45.0ms

prune248.0ms

localize19.0ms

rewrite31.0ms

series129.0ms

simplify113.0ms

prune268.0ms

regimes131.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.0s

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