Details

sample93.0ms

Algorithm

intervals

Results

24.0ms	256×	body	160	nan
23.0ms	530×	body	80	nan
14.0ms	256×	body	80	valid

simplify32.0ms

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: 32.6b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
30.4b	(sqrt (- (* x x) 1.0))

rewrite51.0ms

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:

31.0ms	(+ x (sqrt (- (* x x) 1.0)))
18.0ms	(sqrt (- (* x x) 1.0))

series153.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(+ x (sqrt (- (* x x) 1.0)))
80.0ms	(sqrt (- (* x x) 1.0))

simplify1.5s

Counts

34 → 34

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	91	451
1	216	402
2	541	366
3	1508	358
done	5001	351

prune88.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (- (- x (/ 0.125 (pow x 3))) (/ 0.5 x)))
0.3b	(/ 0.125 (pow x 3))

rewrite490.0ms

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:

472.0ms	(+ x (- (- x (/ 0.125 (pow x 3))) (/ 0.5 x)))
9.0ms	(/ 0.125 (pow x 3))

series121.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(+ x (- (- x (/ 0.125 (pow x 3))) (/ 0.5 x)))
60.0ms	(/ 0.125 (pow x 3))

simplify2.7s

Counts

92 → 92

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	133	1137
1	264	975
2	751	921
3	4399	917
done	5001	917

prune257.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	7613×	body	160	nan
883.0ms	16341×	body	80	nan
466.0ms	8000×	body	80	valid