Details

sample76.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
16.0ms	257×	body	160	nan
15.0ms	534×	body	80	nan

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	11	9
2	12	9
done	12	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`add-cube-cbrt` `sqrt-prod` `add-log-exp`
3×	`pow1` `fma-def`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

19.0ms	(+ x (sqrt (- (* x x) 1.0)))
14.0ms	(sqrt (- (* x x) 1.0))

series146.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(+ x (sqrt (- (* x x) 1.0)))
74.0ms	(sqrt (- (* x x) 1.0))

simplify731.0ms

Counts

41 → 41

Iterations

Useful iterations: done (729.0ms)

Iter	Nodes	Cost
0	95	483
1	244	425
2	969	392
done	5000	356

prune154.0ms

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))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
11×	`*-un-lft-identity`
9×	`associate-r`
7×	`add-cube-cbrt` `associate-l`
6×	`pow1`
4×	`add-exp-log` `frac-times` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `fma-def` `pow-prod-down` `flip--`
2×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `log1p-expm1-u` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 60

Calls

2 calls:

9.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
85.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series486.0ms

Counts

2 → 6

Calls

2 calls:

177.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
309.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.0s

Counts

66 → 66

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	156	1202
1	389	1024
2	1566	951
done	5000	944

prune200.0ms

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

sample3.0s

Algorithm

intervals

Results

832.0ms	8000×	body	80	valid
754.0ms	7557×	body	160	nan
698.0ms	16328×	body	80	nan