Details

sample88.0ms

Algorithm

intervals

Results

17.0ms	35×	body	2560	valid
15.0ms	196×	body	80	valid
12.0ms	31×	body	1280	valid
7.0ms	89×	body	80	nan
3.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
0.0ms	2×	body	320	valid
0.0ms	3×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite126.0ms

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--` `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 → 91

Calls

4 calls:

76.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
60.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1527
1	392
0	158

prune535.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 177

Calls

4 calls:

42.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
10.0ms	(- (* b_2 b_2) (* a c))
26.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
38.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

189 → 189

Iterations

Iter	Nodes
done	5000
2	3515
1	665
0	266

prune890.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.8b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.6b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite262.0ms

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-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`
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 → 187

Calls

4 calls:

54.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
119.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
68.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series682.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
212.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
278.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

199 → 199

Iterations

Iter	Nodes
done	5000
2	4138
1	765
0	304

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.6b	(/ (* a c) a)
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite89.0ms

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×	`sqrt-prod`
3×	`associate-/r*` `times-frac` `flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `difference-of-squares`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
57.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(/ (* a c) a)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b_2 b_2) (* a c))
124.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(/ (* a c) a)
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	1708
1	313
0	125

prune421.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.4b

regimes442.0ms

Accuracy

87.2% (3.6b remaining)

Error of 9.0b against oracle of 5.4b and baseline of 33.8b

bsearch255.0ms

Steps

Iters	Range		Point
10	4.0721326822252617e+40	3.6590220876252264e+50	3.628799960716312e+50
8	7.211886341925621e-305	2.1257753989446086e-302	8.458581803714143e-305
8	-3.854198347822332e+69	-2.1688378611128307e+65	-1.09861951291665e+69

simplify12.0ms

Iterations

Iter	Nodes
done	37
2	37
1	36
0	30

end0.0ms

sample3.1s

Algorithm

intervals

Results

848.0ms	868×	body	1280	valid
538.0ms	5799×	body	80	valid
515.0ms	1136×	body	2560	valid
293.0ms	2815×	body	80	nan
115.0ms	446×	body	640	valid
89.0ms	109×	body	5120	valid
46.0ms	238×	body	320	valid
17.0ms	102×	body	160	valid