Details

sample73.0ms

Algorithm

intervals

Results

11.0ms	176×	body	80	valid
9.0ms	33×	body	2560	valid
6.0ms	29×	body	1280	valid
3.0ms	76×	body	80	nan
3.0ms	8×	body	5120	valid
3.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	5×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune11.0ms

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: 35.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

15.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

96 → 96

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	147	1616
1	342	1521
2	913	1427
3	2534	1421
done	5001	1420

prune164.0ms

Filtered

70 candidates to 96 candidates (-37.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	84	12	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Merged error: 5.7b

Counts

97 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

14.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
6.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

174 → 174

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	257	3976
1	564	3486
2	1326	3213
3	3658	3131
done	5000	3131

prune127.0ms

Filtered

82 candidates to 174 candidates (-112.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	176	10	186

Merged error: 5.6b

Counts

186 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
14.9b	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

67 → 67

Iterations

Useful iterations: 3 (292.0ms)

Iter	Nodes	Cost
0	89	1110
1	207	808
2	622	756
3	1816	748
done	5001	748

prune103.0ms

Filtered

54 candidates to 67 candidates (-24.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	67	10	77

Merged error: 5.6b

Counts

77 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))
21.5b	(sqrt (- (* b_2 b_2) (* 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_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

72 → 72

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	77	1011
1	177	880
2	513	842
3	1337	832
4	3669	826
done	5001	826

prune85.0ms

Filtered

58 candidates to 72 candidates (-24.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	71	11	82

Merged error: 5.6b

Counts

82 → 11

regimes351.0ms

Accuracy

84% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 34.5b

bsearch52.0ms

Steps

Iters	Range		Point
7	2.951159271200378e-80	1.7529870675191086e-78	9.827618726336024e-79
8	-8.704679048448932e+71	-1.0976727662850034e+68	-1.013848001599699e+70

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	38
1	32	38
done	32	38

end0.0ms

sample1.5s

Algorithm

intervals

Results

274.0ms	1069×	body	2560	valid
265.0ms	5829×	body	80	valid
204.0ms	907×	body	1280	valid
137.0ms	2967×	body	80	nan
80.0ms	486×	body	640	valid
40.0ms	130×	body	5120	valid
25.0ms	200×	body	320	valid
8.0ms	101×	body	160	valid

Details

sample73.0ms

simplify23.0ms

prune11.0ms

localize10.0ms

rewrite37.0ms

series67.0ms

simplify1.4s

prune164.0ms

localize10.0ms

rewrite41.0ms

series69.0ms

simplify2.2s

prune127.0ms

localize15.0ms

rewrite30.0ms

series49.0ms

simplify1.1s

prune103.0ms

localize13.0ms

rewrite25.0ms

series55.0ms

simplify2.2s

prune85.0ms

regimes351.0ms

bsearch52.0ms

simplify3.0ms

end0.0ms

sample1.5s

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