Details

sample29.0ms

Algorithm

intervals

Results

5.0ms	48×	body	640	valid
5.0ms	64×	body	1280	valid
4.0ms	278×	body	80	nan
2.0ms	114×	body	80	valid
1.0ms	21×	body	320	valid
0.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite39.0ms

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:

38.0ms

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

series69.0ms

Counts

1 → 3

Calls

1 calls:

69.0ms

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

simplify47.0ms

Counts

22 → 22

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	132	175
1	400	159
2	1559	153
3	5001	149
done	5001	149

prune46.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 55

Calls

2 calls:

29.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
43.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series198.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
134.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify35.0ms

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	295	535
1	1077	482
2	5001	453
done	5001	453

prune119.0ms

Pruning

8 alts after pruning (7 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))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite274.0ms

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:

38.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
36.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
43.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
117.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series774.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
160.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
321.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
136.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify121.0ms

Counts

457 → 457

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	1033	8862
1	4120	7704
2	5001	7681
done	5001	7681

prune565.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
0.3b	(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
0.5b	(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

rewrite418.0ms

Algorithm

rewrite-expression-head

Rules

1804×	`*-un-lft-identity`
1674×	`times-frac`
1600×	`sqrt-prod`
840×	`cbrt-prod`
684×	`add-sqr-sqrt` `add-cube-cbrt`
640×	`distribute-lft-out`
324×	`unpow-prod-down` `cube-prod`
64×	`sqrt-div`
60×	`associate-/r/`
36×	`cube-mult` `unpow3` `associate-/r` `associate-/l` `sqr-pow`
32×	`flip3-+` `flip-+`
30×	`div-inv`
12×	`add-exp-log`
10×	`add-cbrt-cube`
6×	`pow1` `cube-div`
4×	`cbrt-undiv` `cbrt-div` `div-exp` `add-log-exp`
3×	`pow-unpow` `pow-pow`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `associate-/l/` `rem-cube-cbrt`

Counts

4 → 1096

Calls

4 calls:

42.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
168.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
40.0ms	(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
43.0ms	(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

series979.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
143.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
156.0ms	(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
355.0ms	(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

simplify211.0ms

Counts

1108 → 1108

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1936	26487
1	5001	21134
done	5001	21134

prune855.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes45.0ms

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: 0 (0.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5
done	9	5

end0.0ms

sample688.0ms

Algorithm

intervals

Results

136.0ms	1691×	body	1280	valid
135.0ms	8018×	body	80	nan
83.0ms	1335×	body	640	valid
69.0ms	4048×	body	80	valid
28.0ms	618×	body	320	valid
10.0ms	308×	body	160	valid