Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	58×	body	1280	valid
4.0ms	226×	body	80	nan
3.0ms	42×	body	640	valid
2.0ms	123×	body	80	valid
1.0ms	23×	body	320	valid
0.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize8.0ms

Local error

Found 1 expressions with local error:

3.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 19

Calls

1 calls:

21.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series72.0ms

Counts

1 → 3

Calls

1 calls:

72.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify810.0ms

Counts

22 → 22

Iterations

Useful iterations: done (809.0ms)

Iter	Nodes	Cost
0	59	310
1	133	285
2	375	263
3	1352	257
done	5000	255

prune44.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
31×	`distribute-lft-out`
24×	`times-frac` `sqrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 64

Calls

2 calls:

16.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
31.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series207.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
144.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify451.0ms

Counts

70 → 70

Iterations

Useful iterations: done (448.0ms)

Iter	Nodes	Cost
0	139	1225
1	340	985
2	1072	906
done	5000	902

prune135.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

21.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
71.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
24.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series828.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
169.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
146.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
344.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.1s

Counts

457 → 457

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	440	15237
1	1038	12250
2	2846	11578
done	5001	11574

prune564.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

21574×	`sqrt-prod`
14984×	`*-un-lft-identity`
14958×	`times-frac`
5512×	`distribute-lft-out`
5339×	`add-sqr-sqrt`
5338×	`add-cube-cbrt`
438×	`associate-/l*`
402×	`sqrt-div`
370×	`associate-/r/`
186×	`flip3-+` `flip-+`
185×	`div-inv`
33×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 5786

Calls

4 calls:

21.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
265.0ms	(/ (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
24.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
75.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

165.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
139.0ms	(/ (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
327.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
539.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.6s

Counts

5798 → 5798

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	2678	338863
done	5000	338841

prune10.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: done (1.0ms)

Iter	Nodes	Cost
0	9	11
1	12	11
done	12	9

end0.0ms

sample643.0ms

Algorithm

intervals

Results

146.0ms	1746×	body	1280	valid
134.0ms	7984×	body	80	nan
80.0ms	1276×	body	640	valid
75.0ms	4049×	body	80	valid
29.0ms	615×	body	320	valid
10.0ms	314×	body	160	valid