Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	37×	body	2560	valid
7.0ms	195×	body	80	valid
4.0ms	21×	body	1280	valid
3.0ms	81×	body	80	nan
2.0ms	19×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	75	16
4	87	16
5	95	16
done	95	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
2.0ms	(- (* b b) (* (* 3.0 a) c))
10.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
43.0ms	(- (* b b) (* (* 3.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.5s

Counts

72 → 72

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	122	1001
1	307	907
2	1084	805
3	4598	795
done	5000	795

prune204.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.6b	(cbrt c)
1.1b	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
20.6b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 52

Calls

4 calls:

0.0ms	(cbrt c)
0.0ms	(cbrt c)
10.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
3.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series717.0ms

Counts

4 → 12

Calls

4 calls:

363.0ms	(cbrt c)
173.0ms	(cbrt c)
94.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
88.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify2.1s

Counts

64 → 64

Iterations

Useful iterations: 3 (726.0ms)

Iter	Nodes	Cost
0	106	1069
1	260	947
2	833	602
3	3984	592
done	5000	592

prune203.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt c))
0.6b	(cbrt (cbrt c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
20.6b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 58

Calls

4 calls:

1.0ms	(cbrt (cbrt c))
1.0ms	(cbrt (cbrt c))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
4.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(cbrt (cbrt c))
248.0ms	(cbrt (cbrt c))
97.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
90.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

simplify581.0ms

Counts

70 → 70

Iterations

Useful iterations: done (572.0ms)

Iter	Nodes	Cost
0	116	1560
1	278	1382
2	914	1062
done	5001	1050

prune298.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 11.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.1b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite42.0ms

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:

17.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
17.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
80.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts

72 → 72

Iterations

Useful iterations: 3 (305.0ms)

Iter	Nodes	Cost
0	81	1248
1	190	1104
2	599	1036
3	2014	1028
done	5000	1028

prune243.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 11.4b

regimes504.0ms

Accuracy

97% (0.7b remaining)

Error of 12.8b against oracle of 12.1b and baseline of 34.4b

bsearch181.0ms

Steps

Iters	Range	Point
8	3.1150335411271174e+120	2.748976228023721e+123	1.8586636444574517e+123
8	-1.6620648751329665e-144	-7.987297162739508e-149	-8.205355875708696e-149
9	-2.5095870340849847e+160	-2.2087357092495854e+152	-1.327347707720873e+154

Iters

Range

Point

3.1150335411271174e+120

2.748976228023721e+123

1.8586636444574517e+123

-1.6620648751329665e-144

-7.987297162739508e-149

-8.205355875708696e-149

-2.5095870340849847e+160

-2.2087357092495854e+152

-1.327347707720873e+154

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	42	88
1	52	86
done	52	86

end0.0ms

sample1.1s

Algorithm

intervals

Results

239.0ms	1097×	body	2560	valid
221.0ms	5881×	body	80	valid
151.0ms	853×	body	1280	valid
104.0ms	2944×	body	80	nan
64.0ms	470×	body	640	valid
28.0ms	108×	body	5120	valid
22.0ms	213×	body	320	valid
7.0ms	104×	body	160	valid