Details

sample44.0ms

Algorithm

intervals

Results

9.0ms	55×	body	1280	valid
8.0ms	43×	body	640	valid
8.0ms	248×	body	80	nan
4.0ms	124×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	162
1	9	162
2	10	162
done	10	162

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 35

Calls

2 calls:

12.0ms	(sqrt (+ x 1.0))
58.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series172.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(sqrt (+ x 1.0))
116.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.7s

Counts

41 → 41

Iterations

Useful iterations: 2 (160.0ms)

Iter	Nodes	Cost
0	86	12737
1	193	9896
2	539	9452
3	1605	9452
done	5006	9452

prune160.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 29.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.7b	(- (+ x 1.0) x)

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

117×	`*-un-lft-identity`
41×	`distribute-lft-out`
36×	`add-sqr-sqrt` `times-frac` `sqrt-prod`
19×	`add-cube-cbrt`
16×	`distribute-lft-out--`
11×	`add-log-exp`
8×	`difference-of-squares`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
3×	`flip3-+` `flip-+`
2×	`sum-log` `flip3--` `sqrt-div` `diff-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `associate--l+` `div-inv`

Counts

4 → 112

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
36.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
135.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
60.0ms	(- (+ x 1.0) x)

series330.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ x 1.0))
80.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
205.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(- (+ x 1.0) x)

simplify2.0s

Counts

124 → 124

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	188	42967
1	489	35953
2	1696	35146
done	5000	34669

prune468.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

3 → 71

Calls

3 calls:

5.0ms	(sqrt (+ x 1.0))
24.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
37.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series331.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(sqrt (+ x 1.0))
107.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
174.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify3.0s

Counts

80 → 80

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	156	27666
1	371	22188
2	1131	21250
3	3825	20930
done	5066	20930

prune272.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

60.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
36.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
45.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
216.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

443.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
213.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
202.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
229.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify3.1s

Counts

262 → 262

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	310	116171
1	689	93167
2	1879	91659
done	5000	91259

prune884.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes88.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	202
1	9	202
done	9	202

end0.0ms

sample1.9s

Algorithm

intervals

Results

677.0ms	4095×	body	80	valid
359.0ms	1684×	body	1280	valid
346.0ms	7971×	body	80	nan
205.0ms	1253×	body	640	valid
63.0ms	662×	body	320	valid
21.0ms	306×	body	160	valid