Details

sample59.0ms

Algorithm

intervals

Results

11.0ms	31×	body	2560	valid
10.0ms	203×	body	80	valid
5.0ms	24×	body	1280	valid
4.0ms	78×	body	80	nan
3.0ms	18×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	40	13
4	42	13
done	42	13

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

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:

11.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify898.0ms

Counts

103 → 103

Iterations

Useful iterations: 3 (322.0ms)

Iter	Nodes	Cost
0	153	1823
1	368	1737
2	1080	1620
3	3555	1602
done	5000	1602

prune166.0ms

Filtered

73 candidates to 103 candidates (-41.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 6.2b

Counts

104 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

15.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
19.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify684.0ms

Counts

189 → 189

Iterations

Useful iterations: done (677.0ms)

Iter	Nodes	Cost
0	265	4484
1	606	4041
2	2034	3796
done	5001	3614

prune134.0ms

Filtered

86 candidates to 189 candidates (-119.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	190	9	199

Merged error: 6.1b

Counts

199 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.6b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`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 → 187

Calls

4 calls:

8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
13.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series143.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
49.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
62.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify619.0ms

Counts

199 → 199

Iterations

Useful iterations: done (612.0ms)

Iter	Nodes	Cost
0	295	5662
1	704	4914
2	2754	4742
done	5000	4738

prune210.0ms

Filtered

147 candidates to 199 candidates (-35.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	195	4	199
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	198	10	208

Merged error: 6.1b

Counts

208 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.8b	(/ a (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
11.6b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
14×	`difference-of-squares`
11×	`associate-/r/`
10×	`sqrt-prod`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `distribute-lft-out--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/l*`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 127

Calls

4 calls:

8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(/ a (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
11.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
26.0ms	(/ a (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
60.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify589.0ms

Counts

139 → 139

Iterations

Useful iterations: done (585.0ms)

Iter	Nodes	Cost
0	227	3109
1	559	2934
2	2194	2655
done	5001	2623

prune137.0ms

Filtered

107 candidates to 139 candidates (-29.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	139	10	149

Merged error: 6.1b

Counts

149 → 10

regimes318.0ms

Accuracy

87.3% (3.6b remaining)

Error of 9.4b against oracle of 5.8b and baseline of 34.0b

bsearch101.0ms

Steps

Iters	Range	Point
10	1.1487243557305423e+102	3.920821933018458e+112	1.006345097150897e+106
8	-6.270012320702252e-75	-1.3836310266212783e-77	-1.3985012071961824e-77
8	-8.704679048448932e+71	-1.0976727662850034e+68	-3.4566162426370164e+69

Iters

Range

Point

1.1487243557305423e+102

3.920821933018458e+112

1.006345097150897e+106

-6.270012320702252e-75

-1.3836310266212783e-77

-1.3985012071961824e-77

-8.704679048448932e+71

-1.0976727662850034e+68

-3.4566162426370164e+69

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	55
1	36	55
done	36	55

end0.0ms

sample1.6s

Algorithm

intervals

Results

291.0ms	1062×	body	2560	valid
282.0ms	5949×	body	80	valid
192.0ms	856×	body	1280	valid
141.0ms	2987×	body	80	nan
80.0ms	460×	body	640	valid
38.0ms	117×	body	5120	valid
30.0ms	232×	body	320	valid
10.0ms	112×	body	160	valid

Details

sample59.0ms

simplify32.0ms

prune5.0ms

localize11.0ms

rewrite35.0ms

series74.0ms

simplify898.0ms

prune166.0ms

localize11.0ms

rewrite43.0ms

series76.0ms

simplify684.0ms

prune134.0ms

localize11.0ms

rewrite51.0ms

series143.0ms

simplify619.0ms

prune210.0ms

localize12.0ms

rewrite45.0ms

series116.0ms

simplify589.0ms

prune137.0ms

regimes318.0ms

bsearch101.0ms

simplify7.0ms

end0.0ms

sample1.6s

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