Details

sample34.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
4.0ms	22×	body	1280	valid
3.0ms	112×	body	80	nan
2.0ms	16×	body	640	valid
2.0ms	21×	body	320	valid
1.0ms	10×	body	1280	nan
1.0ms	12×	body	640	nan
1.0ms	12×	body	160	valid
1.0ms	7×	body	320	nan
0.0ms	3×	body	160	nan

simplify100.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	29	12
3	41	12
4	58	12
5	63	12
6	71	12
7	86	12
8	114	12
9	127	12
10	129	12
done	129	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
3.0b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.0b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
28×	`times-frac`
19×	`difference-of-squares`
18×	`add-cube-cbrt`
17×	`distribute-lft-out--`
12×	`log-prod`
7×	`add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

22.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
11.0ms	(/ (- x y) (- 1.0 y))
20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
22.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series272.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
38.0ms	(/ (- x y) (- 1.0 y))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
87.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.4s

Counts

120 → 120

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	205	1894
1	488	1792
2	1198	1680
3	3156	1671
done	5000	1670

prune312.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

3.0b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.0b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.8b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
3.8b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
18×	`log-prod`
16×	`*-un-lft-identity`
12×	`sqrt-prod`
8×	`pow1` `add-cube-cbrt` `add-log-exp` `difference-of-squares`
6×	`add-exp-log` `log-pow`
4×	`log-div` `flip3--` `times-frac` `sqrt-div` `add-cbrt-cube` `flip--` `distribute-lft-out--`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `rem-log-exp` `associate--r-`

Counts

4 → 76

Calls

4 calls:

20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
19.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
23.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
21.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
128.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
132.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

simplify1.6s

Counts

88 → 88

Iterations

Useful iterations: 4 (749.0ms)

Iter	Nodes	Cost
0	114	1602
1	229	1530
2	503	1398
3	1242	1382
4	3894	1378
done	5000	1378

prune286.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
3.0b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
69×	`times-frac`
37×	`add-cube-cbrt`
28×	`difference-of-squares`
24×	`log-prod`
20×	`distribute-lft-out--`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
3×	`div-exp` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-sub` `rem-log-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `log-div` `diff-log` `log-pow` `associate--r-`

Counts

4 → 144

Calls

4 calls:

21.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
11.0ms	(/ (- x y) (- 1.0 y))
43.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
37.0ms	(/ (- x y) (- 1.0 y))
129.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
52.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify2.2s

Counts

156 → 156

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	267	2917
1	619	2789
2	1544	2645
3	4251	2593
done	5000	2588

prune399.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
0.1b	(/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))
0.1b	(/ (sqrt (exp 1.0)) (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0))))
3.0b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

603×	`times-frac`
526×	`add-sqr-sqrt`
376×	`*-un-lft-identity`
270×	`sqrt-prod`
252×	`add-cube-cbrt`
112×	`difference-of-squares`
62×	`distribute-lft-out--`
51×	`associate-/r*`
17×	`associate-/l*`
13×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `flip3--` `flip--` `associate-/l/`
3×	`frac-2neg` `div-sub` `clear-num` `associate-/r/`
1×	`sub-neg` `diff-log` `associate--r-`

Counts

4 → 432

Calls

4 calls:

11.0ms	(/ (- x y) (- 1.0 y))
64.0ms	(/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))
55.0ms	(/ (sqrt (exp 1.0)) (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0))))
20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (- x y) (- 1.0 y))
205.0ms	(/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0)))
134.0ms	(/ (sqrt (exp 1.0)) (/ (- 1.0 (/ (- x y) (- 1.0 y))) (sqrt (exp 1.0))))
51.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify3.1s

Counts

444 → 444

Iterations

Useful iterations: 2 (1.6s)

Iter	Nodes	Cost
0	522	13507
1	1239	12632
2	4018	11774
done	5001	11774

prune782.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes187.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.7b

bsearch108.0ms

Steps

Iters	Range		Point
6	3568380.5266111037	20163573.119074974	19835852.98699539
8	-945895839911.4141	-309616365.81694436	-339938991.33710843

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	33	96
1	40	62
done	40	62

end0.0ms

sample1.0s

Algorithm

intervals

Results

212.0ms	5643×	body	80	valid
166.0ms	836×	body	1280	valid
115.0ms	817×	body	640	valid
99.0ms	3821×	body	80	nan
58.0ms	376×	body	1280	nan
44.0ms	459×	body	320	valid
43.0ms	389×	body	640	nan
18.0ms	225×	body	320	nan
16.0ms	245×	body	160	valid
6.0ms	115×	body	160	nan