Details

sample226.0ms

Algorithm

intervals

Results

21.0ms	43×	body	2560	valid
16.0ms	176×	body	80	valid
12.0ms	31×	body	1280	valid
8.0ms	106×	body	80	nan
6.0ms	19×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	22	12
3	28	12
4	29	12
done	29	12

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite217.0ms

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-exp-log` `add-cbrt-cube` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

116.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
63.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
132.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

96 → 96

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	154	1624
1	801	1512
done	5001	1437

prune371.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize9.0ms

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

prune22.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

78.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
9.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
41.0ms	(- (* b_2 b_2) (* a c))
123.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.6s

Counts

174 → 174

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	258	3976
1	1806	3468
done	5000	3371

prune447.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-l`
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` `associate-*r/` `div-exp` `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:

233.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
17.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
42.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

100 → 100

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	162	1633
1	927	1429
done	5000	1300

prune349.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.2b

regimes222.0ms

Accuracy

82.7% (5.9b remaining)

Error of 11.8b against oracle of 5.9b and baseline of 39.8b

bsearch148.0ms

Steps

Iters	Range		Point
6	1.6855676195581707e-170	7.565529323099765e-170	7.455592343308264e-170
10	-1.4318549199647532e+71	-1.1598944120121166e+59	-2.007820467288354e+70

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	40
1	35	38
done	35	38

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.0s	1075×	body	2560	valid
562.0ms	5874×	body	80	valid
314.0ms	885×	body	1280	valid
232.0ms	3008×	body	80	nan
170.0ms	496×	body	640	valid
90.0ms	107×	body	5120	valid
43.0ms	216×	body	320	valid
11.0ms	93×	body	160	valid