Details

sample61.0ms

Algorithm

intervals

Results

10.0ms	33×	body	2560	valid
10.0ms	176×	body	80	valid
7.0ms	29×	body	1280	valid
4.0ms	78×	body	80	nan
3.0ms	16×	body	640	valid
3.0ms	8×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune8.0ms

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: 35.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
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)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 149

Calls

4 calls:

14.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
4.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify873.0ms

Counts

161 → 161

Iterations

Useful iterations: 2 (313.0ms)

Iter	Nodes	Cost
0	277	4079
1	655	3908
2	1963	3756
done	5000	3756

prune345.0ms

Filtered

114 candidates to 161 candidates (-41.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	151	10	161
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	11	162

Merged error: 5.7b

Counts

162 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

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

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

Counts

4 → 60

Calls

4 calls:

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

series62.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms	(- (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)))

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: 3 (291.0ms)

Iter	Nodes	Cost
0	81	1250
1	184	1108
2	581	1048
3	2012	1036
done	5000	1036

prune188.0ms

Filtered

56 candidates to 72 candidates (-28.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	72	11	83

Merged error: 5.7b

Counts

83 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
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)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt a)
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt a)
9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

65 → 65

Iterations

Useful iterations: 3 (458.0ms)

Iter	Nodes	Cost
0	122	925
1	258	838
2	756	774
3	2629	758
done	5001	758

prune129.0ms

Filtered

48 candidates to 65 candidates (-35.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	65	11	76

Merged error: 5.7b

Counts

76 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt a))
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)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

2.0ms	(cbrt (cbrt a))
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)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt (cbrt a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

68 → 68

Iterations

Useful iterations: 3 (482.0ms)

Iter	Nodes	Cost
0	132	968
1	273	878
2	781	812
3	2663	799
done	5000	799

prune103.0ms

Filtered

51 candidates to 68 candidates (-33.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	68	11	79

Merged error: 5.7b

Counts

79 → 11

regimes370.0ms

Accuracy

84.8% (4.4b remaining)

Error of 10.3b against oracle of 5.9b and baseline of 34.5b

bsearch56.0ms

Steps

Iters	Range		Point
7	2.951159271200378e-80	1.7529870675191086e-78	3.6492548177152135e-79
9	-1.5966504054646543e+104	-1.4637683111029664e+99	-4.7868277875676773e+101

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	38
1	30	38
done	30	38

end0.0ms

sample1.7s

Algorithm

intervals

Results

349.0ms	1070×	body	2560	valid
322.0ms	5830×	body	80	valid
238.0ms	906×	body	1280	valid
159.0ms	2972×	body	80	nan
98.0ms	484×	body	640	valid
51.0ms	130×	body	5120	valid
30.0ms	198×	body	320	valid
11.0ms	102×	body	160	valid

Details

sample61.0ms

simplify52.0ms

prune8.0ms

localize11.0ms

rewrite38.0ms

series65.0ms

simplify873.0ms

prune345.0ms

localize14.0ms

rewrite25.0ms

series62.0ms

simplify1.4s

prune188.0ms

localize17.0ms

rewrite20.0ms

series65.0ms

simplify1.7s

prune129.0ms

localize21.0ms

rewrite20.0ms

series72.0ms

simplify1.5s

prune103.0ms

regimes370.0ms

bsearch56.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling