Details

sample63.0ms

Algorithm

intervals

Results

22.0ms	61×	body	1280	valid
12.0ms	272×	body	80	nan
7.0ms	39×	body	640	valid
6.0ms	124×	body	80	valid
2.0ms	16×	body	320	valid
2.0ms	16×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
4.9b	(- (sqrt (+ x 1)) (sqrt x))

rewrite54.0ms

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` `insert-posit16` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 37

Calls

2 calls:

8.0ms	(sqrt (+ x 1))
45.0ms	(- (sqrt (+ x 1)) (sqrt x))

series109.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(sqrt (+ x 1))
82.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.5s

Counts

43 → 43

Iterations

Iter	Nodes
done	5000
3	2219
2	571
1	178
0	81

prune124.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite58.0ms

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

Counts

3 → 78

Calls

3 calls:

4.0ms	(sqrt (+ x 1))
28.0ms	(+ (sqrt (+ x 1)) (sqrt x))
25.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(sqrt (+ x 1))
64.0ms	(+ (sqrt (+ x 1)) (sqrt x))
88.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify933.0ms

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	995
1	266
0	120

prune327.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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))))

rewrite212.0ms

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:

29.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
22.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
47.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
93.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series598.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
132.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
202.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
127.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify2.2s

Counts

475 → 475

Iterations

Iter	Nodes
done	5001
2	3806
1	921
0	364

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.0b	(pow (+ (sqrt (+ x 1)) (sqrt x)) -1/2)
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(/ (pow (+ (sqrt (+ x 1)) (sqrt x)) -1/2) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

217×	`*-un-lft-identity`
168×	`sqrt-prod`
96×	`distribute-lft-out`
90×	`times-frac`
66×	`unpow-prod-down`
50×	`add-sqr-sqrt`
49×	`add-cube-cbrt`
11×	`sqr-pow`
10×	`add-exp-log` `associate-/l*`
9×	`associate-/r*`
7×	`pow1`
6×	`add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `insert-posit16`
3×	`pow-unpow` `flip3-+` `div-exp` `flip-+`
2×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow-exp` `associate-/r/` `pow-div`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `pow-pow` `frac-2neg` `div-inv`

Counts

4 → 183

Calls

4 calls:

36.0ms	(+ (sqrt (+ x 1)) (sqrt x))
41.0ms	(pow (+ (sqrt (+ x 1)) (sqrt x)) -1/2)
21.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
120.0ms	(/ (pow (+ (sqrt (+ x 1)) (sqrt x)) -1/2) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series571.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (sqrt (+ x 1)) (sqrt x))
211.0ms	(pow (+ (sqrt (+ x 1)) (sqrt x)) -1/2)
172.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
112.0ms	(/ (pow (+ (sqrt (+ x 1)) (sqrt x)) -1/2) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.6s

Counts

195 → 195

Iterations

Iter	Nodes
done	5000
2	2062
1	455
0	210

prune788.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	7

end0.0ms

sample2.5s

Algorithm

intervals

Results

731.0ms	4044×	body	80	valid
567.0ms	1761×	body	1280	valid
419.0ms	8083×	body	80	nan
364.0ms	1275×	body	640	valid
116.0ms	595×	body	320	valid
32.0ms	325×	body	160	valid