Details

sample48.0ms

Algorithm

intervals

Results

11.0ms	54×	body	1280	valid
11.0ms	249×	body	80	nan
7.0ms	44×	body	640	valid
5.0ms	121×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	17×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	11
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
4.4b	(- (sqrt (+ x 1)) (sqrt x))

rewrite58.0ms

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:

9.0ms	(sqrt (+ x 1))
48.0ms	(- (sqrt (+ x 1)) (sqrt x))

series120.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(sqrt (+ x 1))
76.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.4s

Counts

43 → 43

Iterations

Iter	Nodes
5	4088
4	1554
3	730
2	352
1	161
0	81

prune300.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

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:

8.0ms	(sqrt (+ x 1))
22.0ms	(+ (sqrt (+ x 1)) (sqrt x))
34.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series225.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(sqrt (+ x 1))
90.0ms	(+ (sqrt (+ x 1)) (sqrt x))
108.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify972.0ms

Counts

87 → 87

Iterations

Iter	Nodes
4	2176
3	1028
2	524
1	238
0	120

prune780.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

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

rewrite201.0ms

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)))
21.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
107.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
30.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series584.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
171.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
80.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
160.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify2.9s

Counts

475 → 475

Iterations

Iter	Nodes
3	4464
2	1609
1	829
0	364

prune4.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.2b	(/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
0.2b	(/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
0.3b	(* (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x))))))

rewrite440.0ms

Algorithm

rewrite-expression-head

Rules

592×	`sqrt-prod`
412×	`*-un-lft-identity`
369×	`times-frac`
342×	`add-sqr-sqrt`
166×	`add-cube-cbrt`
112×	`distribute-lft-out`
110×	`add-exp-log`
88×	`sqrt-pow1`
86×	`pow-flip`
74×	`swap-sqr`
71×	`pow1`
53×	`div-exp`
49×	`unswap-sqr`
44×	`pow1/2`
42×	`associate-r` `associate-l`
38×	`add-cbrt-cube`
33×	`associate-/r*`
32×	`prod-exp`
26×	`sqrt-div`
25×	`pow-prod-up`
18×	`rec-exp` `1-exp` `pow-div`
15×	`cbrt-undiv`
14×	`associate-/r/`
13×	`pow-sqr`
10×	`inv-pow`
9×	`div-inv`
8×	`cbrt-unprod`
7×	`flip3-+` `pow-prod-down` `flip-+` `associate-/l*`
4×	`insert-posit16` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg`
2×	`frac-times` `associate-l/` `associate-r/` `un-div-inv`
1×	`pow2` `pow-plus` `*-commutative`

Counts

4 → 493

Calls

4 calls:

122.0ms	(/ (* (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
54.0ms	(/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
55.0ms	(/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
181.0ms	(* (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x))))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (* (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
212.0ms	(/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
268.0ms	(/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
162.0ms	(* (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x))))))

simplify1.2s

Counts

505 → 505

Iterations

Iter	Nodes
2	2535
1	1171
0	380

prune5.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes70.0ms

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	11
1	11
0	7

end0.0ms

sample2.4s

Algorithm

intervals

Results

946.0ms	7978×	body	80	nan
496.0ms	1712×	body	1280	valid
326.0ms	1260×	body	640	valid
213.0ms	4111×	body	80	valid
118.0ms	605×	body	320	valid
45.0ms	312×	body	160	valid