Details

sample273.0ms

Algorithm

intervals

Results

7.0ms	37×	body	2560	valid
6.0ms	195×	body	80	valid
5.0ms	21×	body	1280	valid
2.0ms	81×	body	80	nan
2.0ms	19×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite63.0ms

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:

34.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
2.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
33.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

96 → 96

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	154	1624
1	362	1526
2	950	1426
3	2675	1422
done	5001	1420

prune247.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

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:

24.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
2.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
32.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

174 → 174

Iterations

Useful iterations: 3 (910.0ms)

Iter	Nodes	Cost
0	258	3976
1	569	3485
2	1339	3208
3	3676	3128
done	5000	3128

prune252.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ -1 (- (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

300×	`times-frac`
243×	`add-sqr-sqrt`
192×	`*-un-lft-identity`
142×	`add-cube-cbrt`
96×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
52×	`associate-/r*`
50×	`difference-of-squares`
28×	`sqrt-prod`
25×	`distribute-lft-out--`
17×	`associate-/r/`
11×	`flip3--` `flip--`
9×	`div-inv`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`neg-mul-1`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `distribute-neg-frac`

Counts

4 → 266

Calls

4 calls:

49.0ms	(/ -1 (- (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
2.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ -1 (- (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
32.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify937.0ms

Counts

278 → 278

Iterations

Useful iterations: 2 (379.0ms)

Iter	Nodes	Cost
0	439	7291
1	835	6841
2	2651	6693
done	5001	6693

prune654.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) 1))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

80.0ms	(* (/ 1 a) (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) 1))
2.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (/ 1 a) (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) 1))
32.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

99 → 99

Iterations

Useful iterations: 3 (827.0ms)

Iter	Nodes	Cost
0	171	1735
1	454	1410
2	1132	1228
3	3164	1222
done	5000	1222

prune198.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes168.0ms

Accuracy

83.4% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.3b

bsearch105.0ms

Steps

Iters	Range		Point
10	3.056596725548563e-78	7.076105677608322e-63	3.446447862996811e-75
10	-1.852183237050365e+100	-1.9127319211193897e+86	-4.123103533644211e+95

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	39
1	33	39
done	33	39

end0.0ms

sample987.0ms

Algorithm

intervals

Results

216.0ms	1099×	body	2560	valid
190.0ms	5881×	body	80	valid
136.0ms	851×	body	1280	valid
88.0ms	2944×	body	80	nan
58.0ms	470×	body	640	valid
25.0ms	109×	body	5120	valid
21.0ms	219×	body	320	valid
6.0ms	98×	body	160	valid