Details

sample81.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
16.0ms	256×	body	160	nan
16.0ms	530×	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: 32.6b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

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:

21.0ms	(+ x (sqrt (- (* x x) 1.0)))
13.0ms	(sqrt (- (* x x) 1.0))

series162.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(+ x (sqrt (- (* x x) 1.0)))
66.0ms	(sqrt (- (* x x) 1.0))

simplify1.7s

Counts

41 → 41

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	95	483
1	233	424
2	608	392
3	1718	355
done	5001	351

prune119.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ 0.125 (pow x 3))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
6×	`add-exp-log`
4×	`cube-mult` `unpow3` `sqr-pow`
3×	`div-exp` `add-cbrt-cube` `associate-/l*`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 67

Calls

1 calls:

13.0ms

(/ 0.125 (pow x 3))

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

(/ 0.125 (pow x 3))

simplify1.9s

Counts

70 → 70

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	98	740
1	169	596
2	471	580
3	2517	580
done	5000	580

prune144.0ms

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	12	14
1	13	14
done	13	14

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	7613×	body	160	nan
833.0ms	16341×	body	80	nan
484.0ms	8000×	body	80	valid