Details

sample146.0ms

Algorithm

intervals

Results

46.0ms	37×	body	1280	valid
27.0ms	32×	body	2560	valid
24.0ms	184×	body	80	valid
13.0ms	108×	body	80	nan
8.0ms	15×	body	640	valid
4.0ms	4×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	44
4	44
3	41
2	32
1	18
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize18.0ms

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))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite387.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 95

Calls

4 calls:

44.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(- (* b_2 b_2) (* a c))
320.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
53.0ms	(- (* b_2 b_2) (* a c))
81.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

107 → 107

Iterations

Iter	Nodes
3	2584
2	1011
1	386
0	162

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.8b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.4b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 188

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
71.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b_2 b_2) (* a c))
227.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
220.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

200 → 200

Iterations

Iter	Nodes
2	2201
1	732
0	306

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.8b	(- (* b_2 b_2) (* a c))
14.9b	(/ a (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-exp-log`
23×	`add-cbrt-cube`
16×	`div-exp`
13×	`prod-exp`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `cbrt-undiv`
6×	`times-frac` `associate-/l*` `add-log-exp`
5×	`associate-/r/` `cbrt-unprod`
4×	`rec-exp` `flip3--` `1-exp` `insert-posit16` `flip--`
3×	`sqrt-prod`
2×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `sqrt-div` `associate-r/` `div-inv` `pow-flip`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-*l/` `inv-pow`

Counts

4 → 93

Calls

4 calls:

152.0ms	(/ 1 (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
15.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(/ a (* a c))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ 1 (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
41.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(/ a (* a c))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify6.7s

Counts

105 → 105

Iterations

Iter	Nodes
3	8384
2	1473
1	446
0	184

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
17.3b	(/ (+ 0 (* a c)) (* a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`flip3--` `sqrt-prod` `insert-posit16` `flip--`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*r/` `associate-/r/` `difference-of-squares` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 71

Calls

4 calls:

37.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(/ (+ 0 (* a c)) (* a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
45.0ms	(- (* b_2 b_2) (* a c))
208.0ms	(/ (+ 0 (* a c)) (* a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify5.5s

Counts

83 → 83

Iterations

Iter	Nodes
3	8255
2	1374
1	400
0	159

prune866.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.8b

regimes482.0ms

Accuracy

82.1% (4.6b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 31.2b

bsearch131.0ms

Steps

Iters	Range		Point
9	1.9710174875302874e+32	1.945305249879839e+37	9.735084379330809e+35
8	-1.4632440505401307e-54	-4.960915650215066e-57	-1.2963906698702263e-56

simplify7.0ms

Iterations

Iter	Nodes
2	29
1	29
0	25

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.1s	2876×	body	80	nan
755.0ms	988×	body	2560	valid
701.0ms	5915×	body	80	valid
602.0ms	945×	body	1280	valid
226.0ms	477×	body	640	valid
110.0ms	111×	body	5120	valid
55.0ms	190×	body	320	valid
22.0ms	114×	body	160	valid