Details

sample111.0ms

Algorithm

intervals

Results

56.0ms	708×	body	80	nan
19.0ms	256×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
2	16
1	12
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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)))

rewrite81.0ms

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×	`sqrt-div` `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 → 65

Calls

2 calls:

25.0ms	(/ (sqrt (- 1.0 (* x x))) x)
54.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series600.0ms

Counts

2 → 6

Calls

2 calls:

191.0ms	(/ (sqrt (- 1.0 (* x x))) x)
410.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	1883
1	444
0	201

prune409.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize24.0ms

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)))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
54×	`times-frac`
52×	`add-sqr-sqrt`
48×	`sqrt-prod`
42×	`add-cube-cbrt`
14×	`associate-/l*`
10×	`sqrt-div`
8×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out` `difference-of-squares`
6×	`pow1` `associate-/r*` `div-inv`
4×	`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 → 132

Calls

4 calls:

20.0ms	(/ (sqrt (- 1.0 (* x x))) x)
21.0ms	(/ (sqrt (- 1.0 (* x x))) x)
86.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
103.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series887.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (sqrt (- 1.0 (* x x))) x)
133.0ms	(/ (sqrt (- 1.0 (* x x))) x)
311.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
299.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.6s

Counts

144 → 144

Iterations

Iter	Nodes
done	5001
2	1959
1	500
0	227

prune995.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.2s	23956×	body	80	nan
1.1s	8000×	body	80	valid