Details

sample46.0ms

Algorithm

intervals

Results

12.0ms	277×	body	160	nan
11.0ms	520×	body	80	nan
7.0ms	256×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
32.3b	(sqrt (- (* x x) 1.0))

rewrite14.0ms

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:

9.0ms	(+ x (sqrt (- (* x x) 1.0)))
5.0ms	(sqrt (- (* x x) 1.0))

series129.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(+ x (sqrt (- (* x x) 1.0)))
57.0ms	(sqrt (- (* x x) 1.0))

simplify1.1s

Counts

34 → 34

Iterations

Useful iterations: 3 (269.0ms)

Iter	Nodes	Cost
0	91	451
1	216	406
2	518	366
3	1531	358
done	5000	358

prune96.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (- (- x (/ 0.125 (pow x 3))) (/ 0.5 x)))
0.4b	(/ 0.125 (pow x 3))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity` `times-frac`
27×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
11×	`add-log-exp`
7×	`add-exp-log`
4×	`cube-mult` `associate-+r+` `unpow3` `add-cbrt-cube` `sqr-pow`
3×	`diff-log` `div-exp` `sum-log` `distribute-lft-out` `associate-/l*` `distribute-lft-out--`
2×	`pow1` `sub-neg` `associate--l+`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+r-` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 86

Calls

2 calls:

252.0ms	(+ x (- (- x (/ 0.125 (pow x 3))) (/ 0.5 x)))
5.0ms	(/ 0.125 (pow x 3))

series85.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+ x (- (- x (/ 0.125 (pow x 3))) (/ 0.5 x)))
40.0ms	(/ 0.125 (pow x 3))

simplify2.2s

Counts

92 → 92

Iterations

Useful iterations: 3 (975.0ms)

Iter	Nodes	Cost
0	133	1137
1	279	975
2	770	921
3	4256	917
done	5000	917

prune160.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	12	14
done	12	14

end0.0ms

sample1.3s

Algorithm

intervals

Results

349.0ms	7725×	body	160	nan
330.0ms	16077×	body	80	nan
227.0ms	8000×	body	80	valid