Details

sample322.0ms

Algorithm

intervals

Results

7.0ms	179×	body	80	valid
7.0ms	38×	body	1280	valid
5.0ms	24×	body	2560	valid
2.0ms	73×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	7×	body	160	valid

simplify11.0ms

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize12.0ms

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))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite110.0ms

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)
8.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

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

prune230.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.9b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.2b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite177.0ms

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))
92.0ms	(/ (/ (+ 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))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* b_2 b_2) (* a c))
155.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
187.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Counts

196 → 196

Iterations

Useful iterations: 2 (79.0ms)

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

prune453.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.8b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
2.9b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
41.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
78.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* b_2 b_2) (* a c))
173.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
136.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify88.0ms

Counts

449 → 449

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1541	7328
1	5002	6762
done	5002	6762

prune976.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `flip--` `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` `associate-/r/` `inv-pow`

Counts

4 → 154

Calls

4 calls:

42.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
43.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
37.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	604	1948
1	2464	1778
2	5001	1652
done	5001	1652

prune233.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.7b

regimes260.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.9b

bsearch126.0ms

Steps

Iters	Range	Point
9	1.4800420954007604e+99	2.6367850541344314e+108	4.3978336183962956e+103
6	1.0058798208127442e-173	1.0693689171863556e-172	1.0274168215380685e-173
10	-6.90058054258779e+154	-1.4735496756669211e+144	-6.483959257496842e+145

Iters

Range

Point

1.4800420954007604e+99

2.6367850541344314e+108

4.3978336183962956e+103

1.0058798208127442e-173

1.0693689171863556e-172

1.0274168215380685e-173

-6.90058054258779e+154

-1.4735496756669211e+144

-6.483959257496842e+145

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	20
1	42	20
2	42	20
done	42	20

end0.0ms

sample1.1s

Algorithm

intervals

Results

195.0ms	1024×	body	2560	valid
191.0ms	5915×	body	80	valid
144.0ms	899×	body	1280	valid
91.0ms	2902×	body	80	nan
53.0ms	449×	body	640	valid
27.0ms	117×	body	5120	valid
23.0ms	236×	body	320	valid
8.0ms	129×	body	160	valid