Details

sample72.0ms

Algorithm

intervals

Results

37.0ms	714×	body	80	nan
12.0ms	256×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	16	13
3	18	13
done	18	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* x x))
0.0b	(/ (sqrt (- 1.0 (* x x))) x)
0.0b	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
42×	`times-frac`
39×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
16×	`sqrt-prod`
13×	`fma-def`
8×	`log-prod` `distribute-lft-out` `add-log-exp`
7×	`add-exp-log` `associate-/l*`
6×	`add-cbrt-cube` `div-inv`
5×	`pow1` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-div` `fma-neg` `prod-diff` `associate-/r*`
2×	`distribute-rgt-out` `flip3--` `flip3-+` `sqrt-div` `frac-add` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `sum-log` `log-pow`

Counts

4 → 122

Calls

4 calls:

6.0ms	(- 1.0 (* x x))
25.0ms	(/ (sqrt (- 1.0 (* x x))) x)
65.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
100.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series779.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- 1.0 (* x x))
174.0ms	(/ (sqrt (- 1.0 (* x x))) x)
403.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
132.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify1.1s

Counts

134 → 134

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	234	1963
1	522	1840
2	1486	1701
done	5000	1676

prune533.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.1b	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.1b	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
56×	`times-frac`
28×	`add-cube-cbrt`
26×	`fma-def`
20×	`sqrt-prod`
16×	`distribute-lft-out`
12×	`hypot-def`
10×	`div-inv`
8×	`add-log-exp`
6×	`pow1` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `distribute-rgt-out` `flip3-+` `frac-add` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 122

Calls

4 calls:

61.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
40.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
87.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
111.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series842.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
130.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
312.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
259.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify3.1s

Counts

134 → 134

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	168	2034
1	418	1880
2	1174	1756
3	4167	1688
done	5000	1684

prune703.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	29
1	12	29
done	12	29

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.4s	24392×	body	80	nan
692.0ms	8000×	body	80	valid