Details

sample331.0ms

Algorithm

intervals

Results

52.0ms	176×	body	80	valid
33.0ms	4×	body	160	valid
24.0ms	43×	body	2560	valid
14.0ms	31×	body	1280	valid
9.0ms	106×	body	80	nan
6.0ms	19×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid

simplify62.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite134.0ms

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:

69.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
42.0ms	(- (* b_2 b_2) (* a c))
81.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

92 → 92

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	151	1534
1	355	1440
2	1001	1266
3	2792	1252
done	5000	1249

prune416.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

localize9.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune14.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite227.0ms

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:

169.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms	(- (* b_2 b_2) (* a c))
30.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
65.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts

96 → 96

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	175	1643
1	438	1441
2	1334	1224
3	4092	1198
done	5000	1198

prune358.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0b	(/ (+ (* a c) 0) a)
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

15.0ms	(- (* b_2 b_2) (* a c))
40.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
48.0ms	(/ (+ (* a c) 0) a)
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b_2 b_2) (* a c))
121.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(/ (+ (* a c) 0) a)
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts

86 → 86

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	148	1154
1	323	982
2	1060	904
3	3700	866
done	5000	866

prune324.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.2b

regimes192.0ms

Accuracy

92.8% (1.7b remaining)

Error of 7.5b against oracle of 5.8b and baseline of 29.0b

bsearch208.0ms

Steps

Iters	Range		Point
9	1.7084993271036838e+35	8.915315724770326e+40	8.75372275402518e+40
9	-4.09118134758863e-163	-1.5699591568311042e-168	-3.385925883276496e-167
10	-1.4318549199647532e+71	-1.1598944120121166e+59	-2.007820467288354e+70

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	56
1	40	56
done	40	56

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.0s	1075×	body	2560	valid
480.0ms	5874×	body	80	valid
339.0ms	885×	body	1280	valid
219.0ms	3008×	body	80	nan
140.0ms	496×	body	640	valid
48.0ms	107×	body	5120	valid
36.0ms	216×	body	320	valid
11.0ms	93×	body	160	valid