Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	40×	body	2560	valid
7.0ms	187×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify45.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	76	16
4	90	16
5	98	16
done	98	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

36.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
20.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
43.0ms	(- (* b b) (* (* 3.0 a) c))
79.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify469.0ms

Counts

84 → 84

Iterations

Useful iterations: done (466.0ms)

Iter	Nodes	Cost
0	154	1592
1	387	1490
2	1317	1334
done	5000	1326

prune232.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b) (* 3.0 a))
0.8b	(- (pow b 2) (* 3.0 (* a c)))
1.3b	(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
21.1b	(sqrt (- (pow b 2) (* 3.0 (* a c))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

72.0ms	(/ (- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b) (* 3.0 a))
7.0ms	(- (pow b 2) (* 3.0 (* a c)))
40.0ms	(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
7.0ms	(sqrt (- (pow b 2) (* 3.0 (* a c))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b) (* 3.0 a))
47.0ms	(- (pow b 2) (* 3.0 (* a c)))
77.0ms	(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
66.0ms	(sqrt (- (pow b 2) (* 3.0 (* a c))))

simplify1.7s

Counts

84 → 84

Iterations

Useful iterations: 3 (433.0ms)

Iter	Nodes	Cost
0	152	1592
1	381	1482
2	1241	1338
3	4846	1326
done	5000	1326

prune207.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
1.3b	(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
21.1b	(sqrt (- (pow b 2) (* 3.0 (* a c))))
21.1b	(sqrt (- (pow b 2) (* 3.0 (* a c))))

rewrite93.0ms

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:

39.0ms	(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
37.0ms	(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
7.0ms	(sqrt (- (pow b 2) (* 3.0 (* a c))))
7.0ms	(sqrt (- (pow b 2) (* 3.0 (* a c))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
78.0ms	(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
65.0ms	(sqrt (- (pow b 2) (* 3.0 (* a c))))
70.0ms	(sqrt (- (pow b 2) (* 3.0 (* a c))))

simplify893.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (212.0ms)

Iter	Nodes	Cost
0	80	1248
1	189	1096
2	593	1040
3	2168	1028
done	5000	1028

prune255.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 3.0 a) c)
0.8b	(- (* b b) (* (* 3.0 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
2.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
43.0ms	(- (* b b) (* (* 3.0 a) c))
78.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify472.0ms

Counts

72 → 72

Iterations

Useful iterations: done (470.0ms)

Iter	Nodes	Cost
0	120	1001
1	283	903
2	1077	825
done	5000	821

prune161.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

regimes311.0ms

Accuracy

83% (4.9b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 34.1b

bsearch91.0ms

Steps

Iters	Range		Point
8	1.3679096689958957e-81	5.608239720335765e-77	3.84613441880261e-81
7	-3.550313394724354e+57	-2.3888623512096697e+55	-3.124283374205192e+57

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	55
1	36	55
done	36	55

end0.0ms

sample1.1s

Algorithm

intervals

Results

223.0ms	1075×	body	2560	valid
212.0ms	5843×	body	80	valid
154.0ms	906×	body	1280	valid
97.0ms	2890×	body	80	nan
61.0ms	453×	body	640	valid
27.0ms	101×	body	5120	valid
23.0ms	234×	body	320	valid
8.0ms	119×	body	160	valid