Details

sample93.0ms

Algorithm

intervals

Results

27.0ms	194×	body	80	valid
20.0ms	37×	body	2560	valid
12.0ms	28×	body	1280	valid
7.0ms	86×	body	80	nan
6.0ms	18×	body	640	valid
4.0ms	5×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	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: 35.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite81.0ms

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:

49.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
106.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms	(- (* b_2 b_2) (* a c))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

107 → 107

Iterations

Iter	Nodes
done	2000
3	2000
2	1049
1	388
0	162

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
4.3b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.4b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite211.0ms

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:

7.0ms	(- (* b_2 b_2) (* a c))
109.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
77.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b_2 b_2) (* a c))
230.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
265.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

200 → 200

Iterations

Iter	Nodes
done	2002
2	2002
1	740
0	306

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize59.0ms

Local error

Found 4 expressions with local error:

6.2b	(/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.7b	(/ (/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
25.0b	(sqrt (- (* b_2 b_2) (* a c)))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
188×	`add-sqr-sqrt`
154×	`*-un-lft-identity`
122×	`add-cube-cbrt`
118×	`sqrt-prod`
36×	`associate-/l*`
32×	`difference-of-squares`
16×	`distribute-lft-out--`
14×	`sqrt-div`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
7×	`flip3--` `flip--`
6×	`pow1` `div-inv`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`flip3-+` `flip-+`

Counts

4 → 239

Calls

4 calls:

80.0ms	(/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
85.0ms	(/ (/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series1.6s

Counts

4 → 12

Calls

4 calls:

704.0ms	(/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
654.0ms	(/ (/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
115.0ms	(sqrt (- (* b_2 b_2) (* a c)))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

251 → 251

Iterations

Iter	Nodes
done	2003
2	2003
1	841
0	357

prune3.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* c a))
4.3b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2)) a)
9.4b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
25.0b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite160.0ms

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:

12.0ms	(- (* b_2 b_2) (* c a))
76.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2)) a)
59.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
8.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series641.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b_2 b_2) (* c a))
229.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2)) a)
267.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
97.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify936.0ms

Counts

200 → 200

Iterations

Iter	Nodes
done	2000
2	2000
1	744
0	308

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

regimes376.0ms

Accuracy

82.4% (4.7b remaining)

Error of 9.9b against oracle of 5.2b and baseline of 31.6b

bsearch160.0ms

Steps

Iters	Range		Point
9	1.1500868835104234e+100	1.1016243770318365e+105	2.5703497435733685e+102
10	-1.094129558870314e-56	-1.2317994276347943e-74	-1.8774910265390396e-73

simplify4.0ms

Iterations

Iter	Nodes
done	34
1	34
0	27

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	1094×	body	2560	valid
852.0ms	5822×	body	80	valid
466.0ms	949×	body	1280	valid
233.0ms	2994×	body	80	nan
149.0ms	445×	body	640	valid
80.0ms	99×	body	5120	valid
56.0ms	224×	body	320	valid
45.0ms	115×	body	160	valid