Details

sample16.0ms

Algorithm

intervals

Results

4.0ms	256×	body	80	valid
4.0ms	234×	body	80	nan

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	6
1	7	6
2	11	6
done	11	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 16

Calls

1 calls:

3.0ms

(sqrt (- 1.0 (* x x)))

series69.0ms

Counts

1 → 3

Calls

1 calls:

69.0ms

(sqrt (- 1.0 (* x x)))

simplify1.2s

Counts

19 → 19

Iterations

Useful iterations: 3 (297.0ms)

Iter	Nodes	Cost
0	67	246
1	155	220
2	483	206
3	2486	202
done	5001	202

prune49.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (sqrt 1.0)))
0.0b	(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

56×	`times-frac`
54×	`add-sqr-sqrt`
52×	`associate-r`
32×	`add-cube-cbrt` `*-un-lft-identity`
28×	`sqrt-prod`
20×	`unpow-prod-down`
12×	`add-exp-log`
9×	`unswap-sqr`
8×	`unpow2` `sqr-pow`
7×	`add-cbrt-cube`
4×	`pow1` `prod-exp` `add-log-exp`
3×	`associate-r/` `div-exp` `associate-l*`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `flip3-+` `pow-prod-down` `frac-add` `pow-exp` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

2 → 92

Calls

2 calls:

25.0ms	(* 1/2 (/ (pow x 2) (sqrt 1.0)))
14.0ms	(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

series404.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(* 1/2 (/ (pow x 2) (sqrt 1.0)))
324.0ms	(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

simplify845.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (269.0ms)

Iter	Nodes	Cost
0	183	1438
1	468	1262
2	1821	1122
done	5000	1122

prune275.0ms

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	17	22
1	20	22
done	20	22

end0.0ms

sample437.0ms

Algorithm

intervals

Results

143.0ms	8000×	body	80	valid
124.0ms	8035×	body	80	nan