Details

sample91.0ms

Algorithm

intervals

Results

24.0ms	67×	body	1280	valid
19.0ms	37×	body	640	valid
18.0ms	270×	body	80	nan
9.0ms	129×	body	80	valid
3.0ms	16×	body	320	valid
1.0ms	7×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize10.0ms

Local error

Found 1 expressions with local error:

2.1b	(- (sqrt (+ x 1)) (sqrt x))

rewrite26.0ms

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` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out`

Counts

1 → 20

Calls

1 calls:

25.0ms

(- (sqrt (+ x 1)) (sqrt x))

series83.0ms

Counts

1 → 3

Calls

1 calls:

83.0ms

(- (sqrt (+ x 1)) (sqrt x))

simplify2.2s

Counts

23 → 23

Iterations

Iter	Nodes
5	3403
4	1249
3	544
2	246
1	106
0	50

prune158.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite84.0ms

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*` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `div-exp` `associate-/r/` `flip-+` `insert-posit16`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

2 → 61

Calls

2 calls:

30.0ms	(+ (sqrt (+ x 1)) (sqrt x))
52.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series159.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(+ (sqrt (+ x 1)) (sqrt x))
96.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify3.8s

Counts

67 → 67

Iterations

Iter	Nodes
5	5658
4	1832
3	866
2	436
1	190
0	90

prune540.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.2b	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

rewrite257.0ms

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*`
17×	`add-exp-log`
15×	`pow1`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube`
8×	`div-exp` `pow-flip`
7×	`sqrt-pow1` `pow1/2`
6×	`pow-div`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`associate-/l/`

Counts

4 → 463

Calls

4 calls:

44.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
45.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
41.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
101.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
147.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
177.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
129.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.2m

Counts

475 → 475

Iterations

Iter	Nodes
3	4119
2	1597
1	839
0	364

prune3.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.3b	(pow (sqrt (+ (sqrt (+ x 1)) (sqrt x))) -2)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`sqrt-prod`
12×	`distribute-lft-out`
9×	`unpow-prod-down`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`pow1`
5×	`add-log-exp`
4×	`add-exp-log`
3×	`pow-unpow` `pow-pow` `add-cbrt-cube` `insert-posit16`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`
1×	`pow-to-exp` `+-commutative` `rem-sqrt-square` `sum-log` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

3 → 61

Calls

3 calls:

20.0ms	(+ (sqrt (+ x 1)) (sqrt x))
20.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
22.0ms	(pow (sqrt (+ (sqrt (+ x 1)) (sqrt x))) -2)

series370.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (sqrt (+ x 1)) (sqrt x))
96.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
226.0ms	(pow (sqrt (+ (sqrt (+ x 1)) (sqrt x))) -2)

simplify902.0ms

Counts

70 → 70

Iterations

Iter	Nodes
3	2440
2	903
1	310
0	129

prune455.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	9
1	9
0	7

end0.0ms

sample1.6s

Algorithm

intervals

Results

578.0ms	7889×	body	80	nan
327.0ms	1778×	body	1280	valid
284.0ms	4118×	body	80	valid
189.0ms	1226×	body	640	valid
62.0ms	585×	body	320	valid
20.0ms	293×	body	160	valid