Details

sample104.0ms

Algorithm

intervals

Results

26.0ms	177×	body	80	valid
24.0ms	37×	body	2560	valid
14.0ms	25×	body	1280	valid
9.0ms	81×	body	80	nan
8.0ms	18×	body	640	valid
3.0ms	9×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify45.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite86.0ms

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:

52.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
18.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
101.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(- (* b_2 b_2) (* a c))
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify889.0ms

Counts

107 → 107

Iterations

Iter	Nodes
3	2560
2	1015
1	388
0	162

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize24.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.8b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite214.0ms

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:

57.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
84.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
56.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series709.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
251.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
286.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify889.0ms

Counts

203 → 203

Iterations

Iter	Nodes
2	2221
1	729
0	308

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize36.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.6b	(* (/ a (cbrt a)) (/ c (cbrt a)))
6.3b	(* (* (/ a (cbrt a)) (/ c (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

300×	`times-frac`
247×	`add-sqr-sqrt`
178×	`*-un-lft-identity`
170×	`associate-r`
140×	`add-cube-cbrt`
131×	`add-exp-log`
96×	`cbrt-prod`
59×	`add-cbrt-cube`
54×	`div-exp`
49×	`prod-exp`
38×	`difference-of-squares`
31×	`cbrt-undiv` `cbrt-unprod`
23×	`associate-l`
22×	`sqrt-prod`
19×	`distribute-lft-out--`
12×	`pow1` `associate-/r/`
9×	`div-inv` `unswap-sqr`
8×	`flip3--` `flip--`
6×	`frac-times` `associate-*l/` `add-log-exp`
5×	`rec-exp` `1-exp`
4×	`pow-prod-down` `associate-*r/` `insert-posit16`
2×	`sqrt-div` `*-commutative`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 313

Calls

4 calls:

49.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
31.0ms	(* (/ a (cbrt a)) (/ c (cbrt a)))
146.0ms	(* (* (/ a (cbrt a)) (/ c (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series625.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
140.0ms	(* (/ a (cbrt a)) (/ c (cbrt a)))
324.0ms	(* (* (/ a (cbrt a)) (/ c (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

325 → 325

Iterations

Iter	Nodes
2	6209
1	1820
0	536

prune4.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize53.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.3b	(* (* a c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
101×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
76×	`associate-r`
60×	`add-cube-cbrt`
39×	`add-exp-log`
25×	`add-cbrt-cube`
20×	`difference-of-squares`
15×	`prod-exp`
13×	`sqrt-prod`
12×	`div-exp`
10×	`pow1` `distribute-lft-out--`
9×	`cbrt-unprod`
8×	`add-log-exp`
6×	`cbrt-undiv` `flip3--` `associate-/r/` `flip--`
4×	`insert-posit16` `div-inv`
3×	`pow-prod-down`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `associate-r/` `-commutative`

Counts

4 → 150

Calls

4 calls:

15.0ms	(- (* b_2 b_2) (* a c))
48.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
103.0ms	(* (* a c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
245.0ms	(* (* a c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify907.0ms

Counts

162 → 162

Iterations

Iter	Nodes
2	2922
1	912
0	293

prune1.7s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.1b

regimes521.0ms

Accuracy

84% (4.3b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 32.6b

bsearch158.0ms

Steps

Iters	Range		Point
6	1.890398075878753e+149	8.723340275486535e+149	5.121074390969514e+149
11	-5.190492772730695e-87	-3.518766096303871e-111	-4.32337788234514e-89

simplify5.0ms

Iterations

Iter	Nodes
2	33
1	33
0	27

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	1121×	body	2560	valid
742.0ms	5782×	body	80	valid
601.0ms	902×	body	1280	valid
304.0ms	2858×	body	80	nan
198.0ms	474×	body	640	valid
130.0ms	225×	body	320	valid
94.0ms	128×	body	5120	valid
22.0ms	108×	body	160	valid