Details

sample290.0ms

Algorithm

intervals

Results

7.0ms	177×	body	80	valid
7.0ms	37×	body	2560	valid
5.0ms	31×	body	1280	valid
3.0ms	92×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify24.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
27.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite73.0ms

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:

35.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
17.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
33.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

96 → 96

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	154	1624
1	362	1526
2	952	1426
3	2689	1422
done	5000	1420

prune248.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
27.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite59.0ms

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:

25.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
19.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

174 → 174

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	258	3976
1	569	3559
2	1578	3208
3	4079	3128
done	5001	3128

prune268.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.9b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

7.0ms

(* -1/2 (/ c b_2))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

(* -1/2 (/ c b_2))

simplify3.8s

Counts

35 → 35

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	68	277
1	166	250
2	428	230
3	1207	230
4	2968	230
done	5000	230

prune70.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.9b

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(* (* -1/2 c) (/ 1 b_2))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
13×	`associate-r` `add-cbrt-cube`
12×	`prod-exp`
9×	`times-frac`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-unprod`
4×	`div-exp`
3×	`pow-prod-down`
2×	`cbrt-undiv` `rec-exp` `1-exp`
1×	`associate-r/` `associate-l` `un-div-inv` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 38

Calls

1 calls:

10.0ms

(* (* -1/2 c) (/ 1 b_2))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(* (* -1/2 c) (/ 1 b_2))

simplify2.6s

Counts

41 → 41

Iterations

Useful iterations: 2 (161.0ms)

Iter	Nodes	Cost
0	84	411
1	245	316
2	835	238
3	2810	238
done	5000	238

prune45.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 3.9b

regimes282.0ms

Accuracy

85.2% (4.2b remaining)

Error of 9.7b against oracle of 5.5b and baseline of 33.8b

bsearch96.0ms

Steps

Iters	Range		Point
11	4.489865195692553e-133	5.932607888300091e-106	2.0569776426586135e-106
8	-6.10058349091927e+155	-9.408528429616011e+151	-7.93152454634662e+153

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	36
1	28	36
done	28	36

end0.0ms

sample1.0s

Algorithm

intervals

Results

203.0ms	5915×	body	80	valid
201.0ms	1046×	body	2560	valid
135.0ms	862×	body	1280	valid
92.0ms	2863×	body	80	nan
58.0ms	450×	body	640	valid
27.0ms	113×	body	5120	valid
22.0ms	233×	body	320	valid
6.0ms	100×	body	160	valid