Details

sample328.0ms

Algorithm

intervals

Results

8.0ms	41×	body	2560	valid
7.0ms	178×	body	80	valid
4.0ms	26×	body	1280	valid
2.0ms	75×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7
done	44	7

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

63.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901
done	5001	901

prune242.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
3.2b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
90.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
56.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
157.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
193.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify103.0ms

Counts

196 → 196

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723
done	5003	2723

prune469.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.3b	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
3.2b	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

3063×	`times-frac`
1685×	`add-sqr-sqrt`
1444×	`*-un-lft-identity`
1204×	`add-cube-cbrt`
240×	`difference-of-squares`
237×	`associate-/l*`
123×	`sqrt-prod`
120×	`distribute-lft-out--`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
6×	`associate-/r*` `add-log-exp`
5×	`pow1`
4×	`associate-/r/`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1022

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
129.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
102.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
105.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify233.0ms

Counts

1034 → 1034

Iterations

Useful iterations: 1 (67.0ms)

Iter	Nodes	Cost
0	4234	21007
1	5001	20420
done	5001	20420

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.3b	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
3.2b	(* (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) (/ 1 a))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

767×	`times-frac`
538×	`add-sqr-sqrt`
399×	`*-un-lft-identity`
305×	`add-cube-cbrt`
215×	`associate-l`
147×	`add-exp-log`
83×	`div-exp`
78×	`difference-of-squares`
42×	`sqrt-prod`
41×	`add-cbrt-cube`
40×	`prod-exp`
39×	`distribute-lft-out--`
22×	`rec-exp` `1-exp` `associate-/l*`
21×	`unswap-sqr`
19×	`cbrt-undiv` `div-inv`
13×	`associate-r`
9×	`pow1`
8×	`cbrt-unprod`
6×	`add-log-exp`
3×	`pow-prod-down` `associate-/r*`
2×	`flip3--` `pow-flip` `sqrt-div` `div-sub` `flip--` `inv-pow`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l/` `clear-num` `associate-/r/` `un-div-inv` `*-commutative` `associate-/l/`

Counts

4 → 446

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
191.0ms	(* (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) (/ 1 a))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
99.0ms	(* (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) (/ 1 a))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify87.0ms

Counts

458 → 458

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2177	5944
1	5001	5520
done	5001	5520

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.3b

regimes194.0ms

Accuracy

89.7% (2.8b remaining)

Error of 8.3b against oracle of 5.5b and baseline of 32.6b

bsearch137.0ms

Steps

Iters	Range		Point
9	5.30600492772346e+88	5.894388948599132e+93	3.9074270084902826e+93
10	1.8932238735467414e-306	6.8449465898973125e-295	2.4210674984134924e-305
8	-1.0178916472141456e+36	-2.96525867903265e+33	-2.4372516198231233e+34

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	22
1	39	22
done	39	22

end0.0ms

sample1.0s

Algorithm

intervals

Results

193.0ms	1061×	body	2560	valid
181.0ms	5876×	body	80	valid
123.0ms	854×	body	1280	valid
86.0ms	2976×	body	80	nan
60.0ms	471×	body	640	valid
28.0ms	113×	body	5120	valid
23.0ms	242×	body	320	valid
7.0ms	125×	body	160	valid