Details

sample115.0ms

Algorithm

intervals

Results

61.0ms	708×	body	80	nan
21.0ms	256×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	312
1	12	312
2	16	312
3	18	312
done	18	312

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
27×	`times-frac`
25×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
16×	`sqrt-prod`
8×	`log-prod`
7×	`associate-/l*`
5×	`add-exp-log`
4×	`add-cbrt-cube` `distribute-lft-out` `difference-of-squares`
3×	`pow1` `log-div` `associate-/r*` `div-inv`
2×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `distribute-rgt-out` `flip3--` `div-exp` `rem-log-exp` `frac-add` `log-pow` `flip-+` `flip--`

Counts

2 → 69

Calls

2 calls:

10.0ms	(/ (sqrt (- 1.0 (* x x))) x)
45.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series590.0ms

Counts

2 → 6

Calls

2 calls:

137.0ms	(/ (sqrt (- 1.0 (* x x))) x)
452.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.8s

Counts

75 → 75

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	205	32374
1	463	27947
2	1907	27490
done	5001	27375

prune364.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
68×	`times-frac`
58×	`*-un-lft-identity`
52×	`sqrt-prod`
42×	`add-cube-cbrt`
14×	`associate-/l*`
12×	`hypot-def`
10×	`sqrt-div`
8×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out` `difference-of-squares`
6×	`pow1` `associate-/r*` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out` `flip3--` `pow1/2` `div-exp` `frac-add` `flip-+` `flip--`

Counts

4 → 152

Calls

4 calls:

19.0ms	(/ (sqrt (- 1.0 (* x x))) x)
20.0ms	(/ (sqrt (- 1.0 (* x x))) x)
110.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
62.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series927.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (sqrt (- 1.0 (* x x))) x)
171.0ms	(/ (sqrt (- 1.0 (* x x))) x)
296.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
270.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify2.5s

Counts

164 → 164

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	231	62786
1	524	54104
2	2015	52548
done	5001	52218

prune1.2s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	392
1	12	392
done	12	392

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.8s	23956×	body	80	nan
1.2s	8000×	body	80	valid