Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	27×	body	2560	valid
6.0ms	181×	body	80	valid
5.0ms	31×	body	1280	valid
2.0ms	21×	body	640	valid
2.0ms	81×	body	80	nan
2.0ms	8×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	40	13
4	42	13
done	42	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

36.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
216.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

103 → 103

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	156	1821
1	368	1727
2	997	1611
3	3176	1595
done	5001	1594

prune237.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.6b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.2b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
44.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
25.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
151.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
184.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify969.0ms

Counts

199 → 199

Iterations

Useful iterations: done (963.0ms)

Iter	Nodes	Cost
0	304	5659
1	725	4896
2	2520	4718
done	5000	4716

prune474.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.8b	(/ a (* a c))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(/ a (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series183.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(/ a (* a c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

75 → 75

Iterations

Useful iterations: 3 (875.0ms)

Iter	Nodes	Cost
0	125	885
1	276	781
2	854	700
3	2796	692
done	5001	692

prune180.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-l`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-r`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `prod-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `diff-log` `associate-*r/` `div-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

50.0ms	(* (/ 1 c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
5.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (/ 1 c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
45.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

100 → 100

Iterations

Useful iterations: 3 (929.0ms)

Iter	Nodes	Cost
0	163	1635
1	402	1448
2	1141	1288
3	3200	1280
done	5000	1280

prune209.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

regimes149.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.9b

bsearch148.0ms

Steps

Iters	Range		Point
10	1.1889782913455773e+76	6.845935134449847e+90	6.74838527698993e+90
8	3.0778477937611473e-255	3.0021351299804193e-252	3.119187438943242e-255
9	-3.410794538153641e+109	-1.852183237050365e+100	-1.56882272369853e+105

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	32	55
1	38	53
done	38	53

end0.0ms

sample994.0ms

Algorithm

intervals

Results

200.0ms	1059×	body	2560	valid
188.0ms	5842×	body	80	valid
140.0ms	911×	body	1280	valid
97.0ms	2942×	body	80	nan
55.0ms	463×	body	640	valid
24.0ms	103×	body	5120	valid
23.0ms	235×	body	320	valid
7.0ms	109×	body	160	valid