Details

sample63.0ms

Algorithm

intervals

Results

10.0ms	33×	body	2560	valid
10.0ms	176×	body	80	valid
8.0ms	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

simplify43.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	79	16
4	92	16
5	100	16
done	100	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)))

rewrite37.0ms

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:

13.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) 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)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
10.0ms	(- (* 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)))

simplify551.0ms

Counts

161 → 161

Iterations

Useful iterations: done (544.0ms)

Iter	Nodes	Cost
0	277	4079
1	660	3918
2	2222	3762
done	5001	3756

prune357.0ms

Filtered

115 candidates to 161 candidates (-40.0%)

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)))

rewrite26.0ms

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)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify683.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (177.0ms)

Iter	Nodes	Cost
0	81	1250
1	186	1124
2	620	1048
3	1981	1036
done	5000	1036

prune189.0ms

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

localize16.0ms

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)))

rewrite21.0ms

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)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt a)
10.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify780.0ms

Counts

65 → 65

Iterations

Useful iterations: 3 (238.0ms)

Iter	Nodes	Cost
0	122	925
1	260	846
2	823	774
3	2739	758
done	5000	758

prune132.0ms

Filtered

49 candidates to 65 candidates (-32.7%)

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)))

rewrite22.0ms

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))
6.0ms	(- (* 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)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt (cbrt a))
10.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify781.0ms

Counts

68 → 68

Iterations

Useful iterations: 3 (242.0ms)

Iter	Nodes	Cost
0	132	968
1	275	887
2	841	812
3	2739	799
done	5001	799

prune105.0ms

Filtered

52 candidates to 68 candidates (-30.8%)

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

regimes368.0ms

Accuracy

84.8% (4.4b remaining)

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

bsearch65.0ms

Steps

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

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample1.8s

Algorithm

intervals

Results

351.0ms	1070×	body	2560	valid
330.0ms	5830×	body	80	valid
250.0ms	906×	body	1280	valid
162.0ms	2972×	body	80	nan
101.0ms	484×	body	640	valid
56.0ms	130×	body	5120	valid
31.0ms	198×	body	320	valid
11.0ms	102×	body	160	valid

Details

sample63.0ms

simplify43.0ms

prune8.0ms

localize11.0ms

rewrite37.0ms

series74.0ms

simplify551.0ms

prune357.0ms

localize14.0ms

rewrite26.0ms

series68.0ms

simplify683.0ms

prune189.0ms

localize16.0ms

rewrite21.0ms

series69.0ms

simplify780.0ms

prune132.0ms

localize21.0ms

rewrite22.0ms

series77.0ms

simplify781.0ms

prune105.0ms

regimes368.0ms

bsearch65.0ms

simplify3.0ms

end0.0ms

sample1.8s

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