Details

sample188.0ms

Algorithm

intervals

Results

68.0ms	74×	body	2560	valid
65.0ms	120×	body	1280	valid
10.0ms	33×	body	640	valid
7.0ms	18×	body	1280	overflowed
6.0ms	316×	pre	80	true
3.0ms	10×	body	640	overflowed
2.0ms	4×	body	2560	overflowed
2.0ms	8×	body	320	overflowed
2.0ms	8×	body	320	valid
1.0ms	16×	body	80	valid
1.0ms	16×	body	80	overflowed
1.0ms	5×	body	160	valid
1.0ms	4×	body	160	overflowed

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	239	24
4	653	24
5	2835	24
done	5001	24

prune4.0ms

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: 60.0b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
1.8b	(- (exp (* a eps)) 1.0)
2.5b	(- (exp (* b eps)) 1.0)
2.7b	(- (exp (* (+ a b) eps)) 1.0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

11.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series44.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
8.0ms	(- (exp (* a eps)) 1.0)
7.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify531.0ms

Counts

88 → 88

Iterations

Useful iterations: done (528.0ms)

Iter	Nodes	Cost
0	143	1364
1	346	1326
2	1270	1196
done	5002	1190

prune138.0ms

Filtered

65 candidates to 88 candidates (-35.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	3	89

Merged error: 47.0b

Counts

89 → 3

localize29.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (exp (* (+ a b) eps)) 1.0)
2.7b	(* (- (exp (* a eps)) 1.0) (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
4.2b	(* (* 1/6 (pow eps 3)) b)
11.6b	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`add-exp-log`
14×	`-un-lft-identity` `associate-l*`
13×	`add-cbrt-cube`
11×	`prod-exp`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`pow1`
6×	`add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`frac-times` `unpow-prod-down` `flip3--` `flip3-+` `associate-*r/` `flip--` `flip-+`
3×	`*-commutative`
2×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-prod-down` `associate-*l/` `pow-exp` `distribute-lft-out--` `unpow2` `difference-of-squares` `sqr-pow`
1×	`sub-neg` `diff-log`

Counts

4 → 94

Calls

4 calls:

5.0ms	(- (exp (* (+ a b) eps)) 1.0)
16.0ms	(* (- (exp (* a eps)) 1.0) (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
7.0ms	(* (* 1/6 (pow eps 3)) b)
9.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (exp (* (+ a b) eps)) 1.0)
63.0ms	(* (- (exp (* a eps)) 1.0) (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
5.0ms	(* (* 1/6 (pow eps 3)) b)
23.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

simplify1.7s

Counts

106 → 106

Iterations

Useful iterations: 2 (828.0ms)

Iter	Nodes	Cost
0	228	2722
1	705	2554
2	3444	2341
done	5001	2341

prune310.0ms

Filtered

72 candidates to 106 candidates (-47.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	6	106
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Merged error: 46.7b

Counts

109 → 8

localize36.0ms

Local error

Found 4 expressions with local error:

11.6b	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))
20.1b	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
20.1b	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
20.1b	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod`
8×	`associate-l`
6×	`cbrt-div` `add-cbrt-cube`
4×	`pow1` `unpow-prod-down` `flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
3×	`pow1/3` `associate-r` `prod-exp`
2×	`associate-*r/` `unpow2` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 70

Calls

4 calls:

9.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))
9.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
9.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
9.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))
64.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
62.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
64.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))

simplify1.0s

Counts

82 → 82

Iterations

Useful iterations: 2 (405.0ms)

Iter	Nodes	Cost
0	146	2943
1	427	2776
2	1752	2558
done	5001	2558

prune598.0ms

Filtered

68 candidates to 82 candidates (-20.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	81	9	90

Merged error: 46.7b

Counts

90 → 9

localize45.0ms

Local error

Found 4 expressions with local error:

20.1b	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
20.1b	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
20.1b	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
20.1b	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

10.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
10.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
10.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
9.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
61.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
64.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))
64.0ms	(cbrt (+ (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))) (* eps b)))

simplify2.0s

Counts

64 → 64

Iterations

Useful iterations: 3 (613.0ms)

Iter	Nodes	Cost
0	89	2880
1	238	2776
2	794	2532
3	3745	2272
done	5000	2272

prune811.0ms

Filtered

64 candidates to 64 candidates (0.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	64	9	73

Merged error: 46.7b

Counts

73 → 9

regimes330.0ms

Accuracy

52.7% (4.0b remaining)

Error of 52.4b against oracle of 48.4b and baseline of 56.8b

bsearch139.0ms

Steps

Iters	Range		Point
9	0.009971872296741319	14848.343200454	0.11914520210130385
5	-1.5116149063123207e+67	-5.390869519443976e+66	-8.689142308994358e+66

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	175
1	76	175
done	76	175

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.3s	2563×	body	2560	valid
1.8s	3421×	body	1280	valid
344.0ms	1070×	body	640	valid
306.0ms	729×	body	1280	overflowed
197.0ms	10079×	pre	80	true
104.0ms	368×	body	640	overflowed
90.0ms	159×	body	2560	overflowed
75.0ms	332×	body	320	valid
38.0ms	549×	body	80	overflowed
37.0ms	185×	body	320	overflowed
34.0ms	480×	body	80	valid
20.0ms	137×	body	160	valid
12.0ms	86×	body	160	overflowed

Details

sample188.0ms

simplify1.3s

prune4.0ms

localize22.0ms

rewrite26.0ms

series44.0ms

simplify531.0ms

prune138.0ms

localize29.0ms

rewrite40.0ms

series105.0ms

simplify1.7s

prune310.0ms

localize36.0ms

rewrite38.0ms

series213.0ms

simplify1.0s

prune598.0ms

localize45.0ms

rewrite39.0ms

series253.0ms

simplify2.0s

prune811.0ms

regimes330.0ms

bsearch139.0ms

simplify6.0ms

end0.0ms

sample5.8s

Profiling