Details

sample138.0ms

Algorithm

intervals

Results

48.0ms	252×	body	160	nan
39.0ms	492×	body	80	nan
26.0ms	256×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
8	2237
7	713
6	239
5	97
4	60
3	35
2	19
1	16
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1)))
27.3b	(sqrt (- (* x x) 1))

rewrite25.0ms

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:

15.0ms	(+ x (sqrt (- (* x x) 1)))
10.0ms	(sqrt (- (* x x) 1))

series121.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(+ x (sqrt (- (* x x) 1)))
51.0ms	(sqrt (- (* x x) 1))

simplify1.8s

Counts

38 → 38

Iterations

Iter	Nodes
4	3053
3	1225
2	471
1	208
0	91

prune282.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
11×	`*-un-lft-identity`
10×	`associate-r`
7×	`associate-l`
6×	`pow1` `add-cube-cbrt`
4×	`frac-times` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `insert-posit16` `difference-of-squares`
1×	`+-commutative` `sum-log` `sqrt-unprod` `difference-of-sqr-1` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 56

Calls

2 calls:

9.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
28.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

series192.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
101.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify3.9s

Counts

62 → 62

Iterations

Iter	Nodes
4	5995
3	1834
2	693
1	295
0	132

prune487.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Iter	Nodes
2	14
1	14
0	9

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.7s	7710×	body	160	nan
1.3s	16236×	body	80	nan
790.0ms	8000×	body	80	valid