Details

sample112.0ms

Algorithm

intervals

Results

39.0ms	240×	body	160	nan
33.0ms	537×	body	80	nan
20.0ms	256×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
8	2000
7	1825
6	472
5	156
4	60
3	35
2	19
1	16
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1)))
28.5b	(sqrt (- (* x x) 1))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity` `sqrt-prod`
5×	`add-sqr-sqrt`
4×	`add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `difference-of-sqr-1` `flip-+` `flip--` `distribute-lft-out`

Counts

2 → 32

Calls

2 calls:

20.0ms	(+ x (sqrt (- (* x x) 1)))
13.0ms	(sqrt (- (* x x) 1))

series121.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(+ x (sqrt (- (* x x) 1)))
57.0ms	(sqrt (- (* x x) 1))

simplify1.0s

Counts

38 → 38

Iterations

Iter	Nodes
done	2000
4	2000
3	1427
2	508
1	208
0	91

prune140.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- x 1))
0.0b	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.4b	(* (sqrt (+ x 1)) (sqrt (- x 1)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`sqrt-prod`
16×	`*-un-lft-identity`
14×	`sqrt-div`
10×	`associate-r`
8×	`pow1` `add-cube-cbrt`
7×	`associate-l`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`frac-times` `flip3-+` `flip3--` `flip-+` `flip--` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down` `insert-posit16`
2×	`difference-of-sqr-1` `associate-l/` `associate-r/` `distribute-lft-out--`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

3 → 76

Calls

3 calls:

5.0ms	(sqrt (- x 1))
7.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
31.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(sqrt (- x 1))
81.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
87.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify954.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	2000
3	2000
2	757
1	331
0	145

prune282.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	9

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.5s	7609×	body	160	nan
1.2s	16421×	body	80	nan
694.0ms	8000×	body	80	valid