Details

sample158.0ms

Algorithm

intervals

Results

98.0ms	789×	body	80	nan
35.0ms	256×	body	80	valid

simplify48.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
3	20
2	18
1	14
0	9

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
0.0b	(/ (sqrt (- 1 (* x x))) x)
0.0b	(sqrt (- 1 (* x x)))
0.0b	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
59×	`times-frac`
50×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
31×	`sqrt-prod`
16×	`distribute-lft-out`
15×	`log-prod`
14×	`div-inv`
13×	`fma-def`
10×	`difference-of-squares`
8×	`associate-/l*`
7×	`add-exp-log`
6×	`pow1` `distribute-rgt-out` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`log-div` `associate-/r*`
2×	`flip3-+` `flip3--` `frac-add` `distribute-rgt1-in` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `log-pow`

Counts

4 → 142

Calls

4 calls:

27.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
18.0ms	(/ (sqrt (- 1 (* x x))) x)
11.0ms	(sqrt (- 1 (* x x)))
32.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

series436.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
111.0ms	(/ (sqrt (- 1 (* x x))) x)
51.0ms	(sqrt (- 1 (* x x)))
90.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

simplify1.3s

Counts

154 → 154

Iterations

Iter	Nodes
done	2000
3	2000
2	1562
1	555
0	247

prune1.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
0.2b	(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
0.2b	(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
0.5b	(* (sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
139×	`sqrt-prod`
138×	`add-sqr-sqrt`
124×	`times-frac`
64×	`distribute-lft-out`
53×	`div-inv`
49×	`add-cube-cbrt`
30×	`sqrt-div`
28×	`swap-sqr`
25×	`distribute-rgt-out`
21×	`pow1`
18×	`associate-r` `associate-l` `hypot-def`
13×	`fma-def`
11×	`flip3-+` `frac-add` `flip-+`
10×	`sqrt-pow1` `pow1/2`
9×	`frac-times`
7×	`distribute-rgt1-in`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 231

Calls

4 calls:

20.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
26.0ms	(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
47.0ms	(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
161.0ms	(* (sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))

series666.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
189.0ms	(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
195.0ms	(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
154.0ms	(* (sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))

simplify1.2s

Counts

243 → 243

Iterations

Iter	Nodes
done	2019
3	2019
2	1312
1	505
0	240

prune2.7s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify8.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.4s	23583×	body	80	nan
1.2s	8000×	body	80	valid