Details

sample34.0ms

Algorithm

intervals

Results

6.0ms	59×	body	1280	valid
6.0ms	282×	body	80	nan
4.0ms	50×	body	640	valid
3.0ms	123×	body	80	valid
1.0ms	18×	body	320	valid
0.0ms	6×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
1.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite77.0ms

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:

6.0ms	(sqrt (+ x 1.0))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series149.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(sqrt (+ x 1.0))
96.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.8s

Counts

41 → 41

Iterations

Iter	Nodes
done	5000
3	2862
2	671
1	193
0	86

prune214.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

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)))

rewrite113.0ms

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:

6.0ms	(sqrt (+ x 1.0))
45.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
60.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series373.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(sqrt (+ x 1.0))
95.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
231.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify956.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1548
1	371
0	156

prune276.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

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

rewrite236.0ms

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-cbrt-cube` `add-exp-log`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

31.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
35.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
104.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

208.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
202.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
461.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
159.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify2.4s

Counts

457 → 457

Iterations

Iter	Nodes
done	5002
2	4125
1	1072
0	442

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

21574×	`sqrt-prod`
15023×	`*-un-lft-identity`
14958×	`times-frac`
5512×	`distribute-lft-out`
5378×	`add-sqr-sqrt`
5377×	`add-cube-cbrt`
584×	`sqrt-div`
555×	`associate-/l*`
292×	`associate-/r/`
147×	`flip3-+` `flip-+`
146×	`div-inv`
33×	`associate-/r*`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`associate-/l/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 5786

Calls

4 calls:

33.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
55.0ms	(/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
435.0ms	(/ (/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
149.0ms	(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

227.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
600.0ms	(/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
200.0ms	(/ (/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
427.0ms	(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify6.9s

Counts

5798 → 5798

Iterations

Iter	Nodes
done	5001
0	2626

prune18.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes64.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample1.9s

Algorithm

intervals

Results

440.0ms	628×	body	320	valid
381.0ms	7994×	body	80	nan
363.0ms	1720×	body	1280	valid
219.0ms	4065×	body	80	valid
194.0ms	1278×	body	640	valid
24.0ms	309×	body	160	valid