Details

sample224.0ms

Algorithm

intervals

Results

45.0ms	81×	body	80	nan
28.0ms	37×	body	2560	valid
27.0ms	177×	body	80	valid
20.0ms	25×	body	1280	valid
9.0ms	18×	body	640	valid
4.0ms	9×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify54.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize24.0ms

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)))

rewrite136.0ms

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:

53.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
31.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
94.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms	(- (* b_2 b_2) (* a c))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

107 → 107

Iterations

Iter	Nodes
3	2560
2	1015
1	388
0	162

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize54.0ms

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)))

rewrite258.0ms

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:

51.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
117.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
70.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
209.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
252.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

203 → 203

Iterations

Iter	Nodes
2	2221
1	729
0	308

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize51.0ms

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)))

rewrite198.0ms

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:

44.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(* (/ a (cbrt a)) (/ c (cbrt a)))
115.0ms	(* (* (/ a (cbrt a)) (/ c (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series724.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
189.0ms	(* (/ a (cbrt a)) (/ c (cbrt a)))
322.0ms	(* (* (/ a (cbrt a)) (/ c (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

325 → 325

Iterations

Iter	Nodes
2	6209
1	1820
0	536

prune4.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize56.0ms

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)))

rewrite138.0ms

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:

14.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
73.0ms	(* (* a c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
220.0ms	(* (* a c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

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

regimes454.0ms

Accuracy

84% (4.3b remaining)

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

bsearch180.0ms

Steps

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

simplify12.0ms

Iterations

Iter	Nodes
2	33
1	33
0	27

end0.0ms

sample4.0s

Algorithm

intervals

Results

953.0ms	1121×	body	2560	valid
789.0ms	5782×	body	80	valid
706.0ms	902×	body	1280	valid
673.0ms	2858×	body	80	nan
312.0ms	474×	body	640	valid
112.0ms	128×	body	5120	valid
79.0ms	225×	body	320	valid
25.0ms	108×	body	160	valid