Details

sample115.0ms

Algorithm

intervals

Results

36.0ms	39×	body	2560	valid
20.0ms	173×	body	80	valid
16.0ms	30×	body	1280	valid
10.0ms	89×	body	80	nan
8.0ms	16×	body	640	valid
5.0ms	5×	body	5120	valid
3.0ms	10×	body	320	valid
1.0ms	6×	body	160	valid

simplify24.0ms

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: 38.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (* b_2 b_2) (* a c))
1.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite515.0ms

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:

458.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
42.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
70.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

107 → 107

Iterations

Iter	Nodes
3	2584
2	1011
1	386
0	162

prune916.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.6b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.3b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
26.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite247.0ms

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` `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 → 191

Calls

4 calls:

40.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
101.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
88.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series683.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
229.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
270.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

203 → 203

Iterations

Iter	Nodes
2	2212
1	728
0	308

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.4b

localize27.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0b	(/ (* a c) a)
26.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

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` `insert-posit16`
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 → 67

Calls

4 calls:

15.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(/ (* a c) a)
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b_2 b_2) (* a c))
84.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(/ (* a c) a)
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

79 → 79

Iterations

Iter	Nodes
3	3328
2	886
1	299
0	129

prune645.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.2b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
26.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

46.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
50.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify751.0ms

Counts

99 → 99

Iterations

Iter	Nodes
3	2246
2	820
1	323
0	151

prune825.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.4b

regimes484.0ms

Accuracy

91.9% (1.9b remaining)

Error of 7.4b against oracle of 5.5b and baseline of 29.3b

bsearch246.0ms

Steps

Iters	Range		Point
9	2.662790715355376e+61	3.00977400694497e+66	4.71744724099961e+65
6	-2.5739886883617177e-303	-2.8059027898901087e-304	-2.851839700712213e-304
9	-229886301330938.94	-710549284.1101115	-227369802444031.66

simplify7.0ms

Iterations

Iter	Nodes
2	35
1	35
0	30

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	1067×	body	2560	valid
771.0ms	5800×	body	80	valid
552.0ms	913×	body	1280	valid
383.0ms	2966×	body	80	nan
262.0ms	446×	body	640	valid
118.0ms	120×	body	5120	valid
76.0ms	247×	body	320	valid
26.0ms	121×	body	160	valid