Details

sample300.0ms

Algorithm

intervals

Results

35.0ms	10×	body	320	valid
20.0ms	39×	body	2560	valid
14.0ms	173×	body	80	valid
13.0ms	30×	body	1280	valid
9.0ms	89×	body	80	nan
5.0ms	16×	body	640	valid
3.0ms	5×	body	5120	valid
1.0ms	6×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	49
4	49
3	46
2	33
1	19
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize23.0ms

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)))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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 → 175

Calls

4 calls:

84.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
58.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
41.0ms	(- (* b_2 b_2) (* a c))
87.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

187 → 187

Iterations

Iter	Nodes
3	4034
2	1423
1	576
0	248

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.4b

localize9.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
1	0
0	0

prune33.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.4b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 173

Calls

4 calls:

85.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
17.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
57.0ms	(- (* b_2 b_2) (* a c))
86.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.6s

Counts

185 → 185

Iterations

Iter	Nodes
3	4231
2	1607
1	637
0	267

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.4b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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 → 261

Calls

4 calls:

37.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
52.0ms	(- (* b_2 b_2) (* a c))
86.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

273 → 273

Iterations

Iter	Nodes
2	2075
1	834
0	355

prune1.5s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.4b

regimes420.0ms

Accuracy

89.7% (3.5b remaining)

Error of 9.0b against oracle of 5.5b and baseline of 39.3b

bsearch188.0ms

Steps

Iters	Range		Point
9	2.662790715355376e+61	3.00977400694497e+66	4.71744724099961e+65
6	-3.5211401479992753e-265	-6.296270729897811e-266	-2.915349047648131e-265
9	-229886301330938.94	-710549284.1101115	-6239046376.848015

simplify6.0ms

Iterations

Iter	Nodes
2	37
1	37
0	32

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.1s	2966×	body	80	nan
862.0ms	1067×	body	2560	valid
646.0ms	5800×	body	80	valid
601.0ms	913×	body	1280	valid
217.0ms	446×	body	640	valid
141.0ms	247×	body	320	valid
125.0ms	120×	body	5120	valid
50.0ms	121×	body	160	valid