Details

sample104.0ms

Algorithm

intervals

Results

28.0ms	257×	body	160	nan
26.0ms	534×	body	80	nan
16.0ms	256×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	11	9
done	11	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
29.7b	(sqrt (- (* x x) 1.0))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

33.0ms	(+ x (sqrt (- (* x x) 1.0)))
45.0ms	(sqrt (- (* x x) 1.0))

series180.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(+ x (sqrt (- (* x x) 1.0)))
85.0ms	(sqrt (- (* x x) 1.0))

simplify487.0ms

Counts

34 → 34

Iterations

Useful iterations: done (486.0ms)

Iter	Nodes	Cost
0	91	451
1	225	402
2	885	366
done	5001	358

prune113.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 53

Calls

2 calls:

6.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
56.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series436.0ms

Counts

2 → 6

Calls

2 calls:

187.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
249.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify775.0ms

Counts

59 → 59

Iterations

Useful iterations: 2 (221.0ms)

Iter	Nodes	Cost
0	152	1150
1	367	981
2	1451	924
done	5000	924

prune210.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
done	13	14

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	16328×	body	80	nan
843.0ms	7557×	body	160	nan
495.0ms	8000×	body	80	valid