Details

sample81.0ms

Algorithm

intervals

Results

22.0ms	62×	body	1280	valid
19.0ms	243×	body	80	nan
11.0ms	42×	body	640	valid
9.0ms	123×	body	80	valid
4.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.4b	(- (sqrt (+ x 1)) (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` `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))
67.0ms	(- (sqrt (+ x 1)) (sqrt x))

series113.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(sqrt (+ x 1))
87.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.8s

Counts

43 → 43

Iterations

Iter	Nodes
5	4263
4	1592
3	732
2	350
1	159
0	81

prune316.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)))

rewrite95.0ms

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))
38.0ms	(+ (sqrt (+ x 1)) (sqrt x))
47.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series193.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(sqrt (+ x 1))
68.0ms	(+ (sqrt (+ x 1)) (sqrt x))
85.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.5s

Counts

87 → 87

Iterations

Iter	Nodes
4	2183
3	1035
2	523
1	237
0	120

prune738.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.3b	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

308×	`*-un-lft-identity`
290×	`sqrt-prod`
168×	`times-frac`
136×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
43×	`swap-sqr`
31×	`pow1`
27×	`sqrt-pow1` `associate-r` `associate-l`
16×	`unswap-sqr`
14×	`add-exp-log` `associate-/r/`
12×	`associate-/r*`
11×	`pow-flip` `inv-pow`
10×	`add-cbrt-cube`
9×	`pow1/2` `pow-prod-up` `div-inv`
7×	`flip3-+` `flip-+`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-down` `pow-sqr`
4×	`div-exp` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 282

Calls

4 calls:

30.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
52.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
53.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
165.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
114.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
83.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
72.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

simplify1.1s

Counts

294 → 294

Iterations

Iter	Nodes
3	2040
2	881
1	442
0	229

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
82×	`sqrt-prod`
47×	`times-frac`
40×	`distribute-lft-out`
35×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
15×	`associate-/r*`
13×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1`
6×	`sqrt-div` `associate-/r/`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `div-exp` `flip-+` `insert-posit16` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `div-inv`
2×	`clear-num` `frac-2neg` `pow1/2` `pow-flip` `inv-pow`
1×	`rec-exp` `sqrt-undiv` `sqrt-unprod` `1-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`

Counts

4 → 143

Calls

4 calls:

21.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
38.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
27.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
88.0ms	(/ (* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt 1)) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series430.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
157.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
80.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
89.0ms	(/ (* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt 1)) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify17.4s

Counts

155 → 155

Iterations

Iter	Nodes
3	3036
2	962
1	417
0	195

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes44.0ms

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
2	11
1	11
0	9

end0.0ms

sample1.9s

Algorithm

intervals

Results

505.0ms	1749×	body	1280	valid
477.0ms	7976×	body	80	nan
306.0ms	1292×	body	640	valid
290.0ms	4070×	body	80	valid
83.0ms	588×	body	320	valid
28.0ms	301×	body	160	valid