Details

sample117.0ms

Algorithm

intervals

Results

11.0ms	43×	body	2560	valid
9.0ms	164×	body	80	valid
6.0ms	32×	body	1280	valid
3.0ms	80×	body	80	nan
3.0ms	16×	body	640	valid
3.0ms	8×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	6×	body	160	valid

simplify354.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	10	283
1	14	283
2	22	243
3	25	243
4	27	243
5	29	243
done	29	243

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.4b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite176.0ms

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×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

12.0ms	(- (* b_2 b_2) (* a c))
93.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
52.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b_2 b_2) (* a c))
154.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
112.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
132.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

96 → 96

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	154	33768
1	384	30653
2	1463	30453
done	5000	30413

prune644.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize6.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune56.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.4b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`associate-r` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 85

Calls

4 calls:

12.0ms	(- (* b_2 b_2) (* a c))
170.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
33.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* b_2 b_2) (* a c))
141.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
78.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.7s

Counts

97 → 97

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	174	33022
1	453	28023
2	2716	26591
done	5001	26431

prune522.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.4b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`associate-l` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-r`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `prod-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `diff-log` `div-exp` `associate-*r/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

12.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
67.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* b_2 b_2) (* a c))
182.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
120.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

100 → 100

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	162	33222
1	439	29009
2	2232	27166
done	5001	27006

prune433.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

regimes399.0ms

Accuracy

87.8% (4.2b remaining)

Error of 9.4b against oracle of 5.2b and baseline of 39.5b

bsearch69.0ms

Steps

Iters	Range		Point
2	3.964947473899983e-62	4.720485511979589e-62	4.626043257219638e-62
7	-5.856362438573669e+138	-1.280729871585891e+137	-3.450829996567048e+138

simplify9.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	24	748
1	28	748
done	28	748

end0.0ms

sample2.8s

Algorithm

intervals

Results

677.0ms	1095×	body	2560	valid
587.0ms	470×	body	640	valid
498.0ms	5788×	body	80	valid
301.0ms	885×	body	1280	valid
212.0ms	2874×	body	80	nan
50.0ms	110×	body	5120	valid
41.0ms	244×	body	320	valid
13.0ms	116×	body	160	valid