Details

sample52.0ms

Algorithm

intervals

Results

12.0ms	55×	body	1280	valid
11.0ms	278×	body	80	nan
6.0ms	39×	body	640	valid
6.0ms	134×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.8b	(- (sqrt (+ x 1)) (sqrt x))

rewrite40.0ms

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:

5.0ms	(sqrt (+ x 1))
35.0ms	(- (sqrt (+ x 1)) (sqrt x))

series116.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(sqrt (+ x 1))
89.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify3.0s

Counts

43 → 43

Iterations

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

prune336.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

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)))

rewrite78.0ms

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:

9.0ms	(sqrt (+ x 1))
37.0ms	(+ (sqrt (+ x 1)) (sqrt x))
30.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series208.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1))
84.0ms	(+ (sqrt (+ x 1)) (sqrt x))
94.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.7s

Counts

87 → 87

Iterations

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

prune746.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

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))))

rewrite214.0ms

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:

45.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
29.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
91.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
35.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series604.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
167.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
105.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
174.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.2m

Counts

475 → 475

Iterations

Iter	Nodes
3	4315
2	1631
1	829
0	364

prune3.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
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)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

4.0ms	(sqrt (+ x 1))
17.0ms	(+ (sqrt (+ x 1)) (sqrt x))
22.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
22.0ms	(pow (sqrt (+ (sqrt (+ x 1)) (sqrt x))) -2)

series389.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (+ x 1))
50.0ms	(+ (sqrt (+ x 1)) (sqrt x))
95.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
221.0ms	(pow (sqrt (+ (sqrt (+ x 1)) (sqrt x))) -2)

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
3	2681
2	1003
1	360
0	158

prune547.0ms

Pruning

10 alts after pruning (8 fresh and 2 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

simplify1.0ms

Iterations

Iter	Nodes
2	9
1	9
0	7

end0.0ms

sample1.6s

Algorithm

intervals

Results

623.0ms	1698×	body	1280	valid
311.0ms	8086×	body	80	nan
215.0ms	1266×	body	640	valid
194.0ms	4089×	body	80	valid
88.0ms	650×	body	320	valid
20.0ms	297×	body	160	valid