Details

sample74.0ms

Algorithm

intervals

Results

28.0ms	276×	body	80	valid
7.0ms	78×	body	80	nan

simplify100.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	20	38
1	35	38
2	65	37
3	114	37
4	136	37
5	148	37
6	149	37
done	149	37

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 18.2b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.7b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 57

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

69 → 69

Iterations

Useful iterations: 3 (374.0ms)

Iter	Nodes	Cost
0	91	1130
1	203	1004
2	669	944
3	2445	936
done	5000	936

prune194.0ms

Filtered

53 candidates to 69 candidates (-30.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	8	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 8.2b

Counts

70 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`sqrt-prod`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`difference-of-squares`
1×	`sub-neg` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

8.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

72 → 72

Iterations

Useful iterations: 3 (300.0ms)

Iter	Nodes	Cost
0	81	1195
1	184	1036
2	581	994
3	2012	984
done	5000	984

prune245.0ms

Filtered

58 candidates to 72 candidates (-24.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Merged error: 8.2b

Counts

80 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

72 → 72

Iterations

Useful iterations: 3 (234.0ms)

Iter	Nodes	Cost
0	53	1140
1	127	1012
2	420	940
3	1644	932
done	5000	932

prune356.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	72	9	81

Merged error: 8.2b

Counts

81 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

11.0b	(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 53

Calls

4 calls:

9.0ms	(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
31.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

65 → 65

Iterations

Useful iterations: 3 (552.0ms)

Iter	Nodes	Cost
0	151	1492
1	348	1412
2	1022	1194
3	3473	1147
done	5000	1147

prune209.0ms

Filtered

56 candidates to 65 candidates (-16.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	64	10	74

Merged error: 8.2b

Counts

74 → 10

regimes318.0ms

Accuracy

91.7% (1.0b remaining)

Error of 9.0b against oracle of 8.0b and baseline of 20.3b

bsearch66.0ms

Steps

Iters	Range		Point
6	1.1487243557305423e+102	6.148420459531844e+102	1.1692565862096847e+102
9	-1.589409284886386e+110	-1.5966504054646543e+104	-1.5601353151121372e+110

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	132
1	47	132
done	47	132

end0.0ms

sample1.5s

Algorithm

intervals

Results

806.0ms	8720×	body	80	valid
263.0ms	2972×	body	80	nan

Details

sample74.0ms

simplify100.0ms

prune13.0ms

localize23.0ms

rewrite25.0ms

series69.0ms

simplify1.4s

prune194.0ms

localize24.0ms

rewrite25.0ms

series61.0ms

simplify1.5s

prune245.0ms

localize33.0ms

rewrite20.0ms

series60.0ms

simplify1.5s

prune356.0ms

localize27.0ms

rewrite23.0ms

series108.0ms

simplify1.4s

prune209.0ms

regimes318.0ms

bsearch66.0ms

simplify4.0ms

end0.0ms

sample1.5s

Profiling