Details

sample173.0ms

Algorithm

intervals

Results

108.0ms	789×	body	80	nan
38.0ms	256×	body	80	valid

simplify33.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	18
2	18
1	14
0	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
50×	`times-frac`
43×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `sqrt-prod`
16×	`distribute-lft-out`
15×	`log-prod`
13×	`div-inv`
10×	`difference-of-squares`
8×	`associate-/l*`
7×	`add-exp-log`
6×	`pow1` `distribute-rgt-out` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `insert-posit16`
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 → 121

Calls

4 calls:

28.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
15.0ms	(/ (sqrt (- 1 (* x x))) x)
7.0ms	(sqrt (- 1 (* x x)))
16.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

series525.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
147.0ms	(/ (sqrt (- 1 (* x x))) x)
56.0ms	(sqrt (- 1 (* x x)))
92.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

simplify1.2s

Counts

133 → 133

Iterations

Iter	Nodes
done	2000
3	2000
2	1397
1	525
0	239

prune440.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize28.0ms

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))))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
133×	`sqrt-prod`
91×	`times-frac`
77×	`add-sqr-sqrt`
64×	`distribute-lft-out`
52×	`div-inv`
42×	`add-cube-cbrt`
30×	`sqrt-div`
28×	`swap-sqr`
25×	`distribute-rgt-out`
21×	`pow1`
18×	`associate-r` `associate-l`
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×	`insert-posit16` `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 → 192

Calls

4 calls:

16.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
32.0ms	(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
33.0ms	(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
149.0ms	(* (sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
138.0ms	(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
144.0ms	(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
131.0ms	(* (sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))

simplify1.0s

Counts

204 → 204

Iterations

Iter	Nodes
done	2003
3	2003
2	1198
1	490
0	234

prune803.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.2s	23583×	body	80	nan
1.0s	8000×	body	80	valid