Details

sample61.0ms

Algorithm

intervals

Results

11.0ms	176×	body	80	valid
9.0ms	33×	body	2560	valid
6.0ms	29×	body	1280	valid
4.0ms	76×	body	80	nan
3.0ms	16×	body	640	valid
3.0ms	8×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	5×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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)))

rewrite32.0ms

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:

10.0ms	(/ (- (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)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
9.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify686.0ms

Counts

96 → 96

Iterations

Useful iterations: done (683.0ms)

Iter	Nodes	Cost
0	147	1616
1	344	1521
2	965	1427
3	2592	1417
done	5001	1416

prune173.0ms

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)))

rewrite44.0ms

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:

15.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 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)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify448.0ms

Counts

174 → 174

Iterations

Useful iterations: done (443.0ms)

Iter	Nodes	Cost
0	257	3976
1	575	3560
2	1873	3213
done	5001	3193

prune136.0ms

Filtered

83 candidates to 174 candidates (-109.6%)

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

localize12.0ms

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))
16.0ms	(- (* (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)))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* 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)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify596.0ms

Counts

67 → 67

Iterations

Useful iterations: done (594.0ms)

Iter	Nodes	Cost
0	89	1110
1	209	808
2	633	756
3	1760	748
done	5000	746

prune107.0ms

Filtered

54 candidates to 67 candidates (-24.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	67	10	77

Merged error: 5.6b

Counts

77 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.5b	(/ (/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0b	(/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
97×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
21×	`associate-/l*`
16×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`div-inv` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp`
3×	`flip3--` `div-sub` `sqrt-prod` `flip--` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 154

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(/ (/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
16.0ms	(/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
33.0ms	(/ (/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
45.0ms	(/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify570.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (214.0ms)

Iter	Nodes	Cost
0	273	5200
1	711	4581
2	2520	3991
done	5001	3991

prune192.0ms

Filtered

127 candidates to 166 candidates (-30.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	166	10	176

Merged error: 5.6b

Counts

176 → 10

regimes364.0ms

Accuracy

82.5% (4.7b remaining)

Error of 10.4b against oracle of 5.7b and baseline of 32.4b

bsearch53.0ms

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

sample1.6s

Algorithm

intervals

Results

295.0ms	1069×	body	2560	valid
281.0ms	5829×	body	80	valid
210.0ms	907×	body	1280	valid
137.0ms	2967×	body	80	nan
87.0ms	486×	body	640	valid
45.0ms	130×	body	5120	valid
26.0ms	200×	body	320	valid
9.0ms	101×	body	160	valid

Details

sample61.0ms

simplify32.0ms

prune11.0ms

localize10.0ms

rewrite32.0ms

series77.0ms

simplify686.0ms

prune173.0ms

localize10.0ms

rewrite44.0ms

series74.0ms

simplify448.0ms

prune136.0ms

localize12.0ms

rewrite30.0ms

series54.0ms

simplify596.0ms

prune107.0ms

localize15.0ms

rewrite49.0ms

series99.0ms

simplify570.0ms

prune192.0ms

regimes364.0ms

bsearch53.0ms

simplify3.0ms

end0.0ms

sample1.6s

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