Details

sample285.0ms

Algorithm

intervals

Results

8.0ms	194×	body	80	valid
7.0ms	40×	body	2560	valid
4.0ms	28×	body	1280	valid
2.0ms	76×	body	80	nan
1.0ms	10×	body	640	valid
0.0ms	2×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify21.0ms

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: 34.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.4b	(- (* b_2 b_2) (* a c))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

33.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

92 → 92

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	151	1534
1	358	1440
2	1008	1266
3	3130	1252
done	5001	1251

prune233.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.2b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.4b	(- (* b_2 b_2) (* a c))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`prod-exp` `distribute-lft-out`
3×	`flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `sum-log` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 84

Calls

4 calls:

50.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
11.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

96 → 96

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	175	1643
1	447	1441
2	1305	1224
3	4714	1198
done	5000	1198

prune227.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
0.4b	(- (* b_2 b_2) (* a c))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `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`

Counts

4 → 54

Calls

4 calls:

2.0ms	(- (* b_2 b_2) (* a c))
2.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
37.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

66 → 66

Iterations

Useful iterations: 4 (889.0ms)

Iter	Nodes	Cost
0	58	826
1	140	762
2	411	678
3	1192	678
4	3765	676
done	5000	676

prune213.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

69 → 69

Iterations

Useful iterations: 4 (883.0ms)

Iter	Nodes	Cost
0	58	891
1	140	805
2	411	727
3	1192	727
4	3765	724
done	5000	724

prune216.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.7b

regimes207.0ms

Accuracy

90.3% (2.8b remaining)

Error of 8.6b against oracle of 5.8b and baseline of 34.3b

bsearch158.0ms

Steps

Iters	Range	Point
8	1.5276508475467709e+44	4.1560730947117816e+46	4.0029022431090705e+44
10	9.410701402418836e-271	4.7345175229648096e-260	2.2009669688403957e-265
11	-1.829086240692416e+154	-2.187052964502477e+134	-1.0524969308880696e+141

Iters

Range

Point

1.5276508475467709e+44

4.1560730947117816e+46

4.0029022431090705e+44

9.410701402418836e-271

4.7345175229648096e-260

2.2009669688403957e-265

-1.829086240692416e+154

-2.187052964502477e+134

-1.0524969308880696e+141

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	35	62
1	43	60
done	43	60

end0.0ms

sample989.0ms

Algorithm

intervals

Results

215.0ms	1107×	body	2560	valid
195.0ms	5865×	body	80	valid
140.0ms	908×	body	1280	valid
90.0ms	2861×	body	80	nan
55.0ms	422×	body	640	valid
23.0ms	97×	body	5120	valid
20.0ms	216×	body	320	valid
7.0ms	117×	body	160	valid