Details

sample131.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
17.0ms	230×	body	80	nan

simplify89.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	19	11
3	21	11
done	21	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(/ (- 1.0 x) (+ 1.0 x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
24×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

3 → 91

Calls

3 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
19.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
49.0ms	(/ (- 1.0 x) (+ 1.0 x))

series211.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
143.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
60.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify761.0ms

Counts

100 → 100

Iterations

Useful iterations: done (754.0ms)

Iter	Nodes	Cost
0	162	1425
1	348	1350
2	1255	1262
done	5000	1258

prune346.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
56×	`times-frac`
52×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
17×	`sqrt-prod`
16×	`distribute-lft-out`
14×	`distribute-lft-out--`
12×	`associate-/r/`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `difference-of-squares`
6×	`distribute-rgt-out--` `flip3-+` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 125

Calls

4 calls:

113.0ms	(sqrt (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x))))
11.0ms	(/ x (+ 1.0 x))
17.0ms	(/ 1.0 (+ 1.0 x))
139.0ms	(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(sqrt (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x))))
46.0ms	(/ x (+ 1.0 x))
39.0ms	(/ 1.0 (+ 1.0 x))
71.0ms	(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))

simplify1.2s

Counts

137 → 137

Iterations

Useful iterations: 2 (388.0ms)

Iter	Nodes	Cost
0	214	1977
1	480	1851
2	1881	1763
done	5001	1763

prune517.0ms

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	(/ 1.0 (+ 1.0 x))
0.0b	(cbrt (pow (/ 1.0 (+ 1.0 x)) 3))
0.0b	(- (cbrt (pow (/ 1.0 (+ 1.0 x)) 3)) (/ x (+ 1.0 x)))
0.0b	(pow (/ 1.0 (+ 1.0 x)) 3)

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
81×	`*-un-lft-identity`
71×	`times-frac`
54×	`cbrt-prod`
47×	`add-cube-cbrt`
40×	`unpow-prod-down` `cube-prod`
16×	`distribute-lft-out`
14×	`difference-of-squares`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
4×	`associate-/r*` `sqr-pow`
3×	`cube-div` `pow-unpow` `associate-/l*`
2×	`cbrt-undiv` `cube-mult` `cbrt-div` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `frac-sub` `flip--` `rem-cbrt-cube` `distribute-lft-out--`

Counts

4 → 169

Calls

4 calls:

11.0ms	(/ 1.0 (+ 1.0 x))
21.0ms	(cbrt (pow (/ 1.0 (+ 1.0 x)) 3))
245.0ms	(- (cbrt (pow (/ 1.0 (+ 1.0 x)) 3)) (/ x (+ 1.0 x)))
20.0ms	(pow (/ 1.0 (+ 1.0 x)) 3)

series220.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1.0 (+ 1.0 x))
34.0ms	(cbrt (pow (/ 1.0 (+ 1.0 x)) 3))
82.0ms	(- (cbrt (pow (/ 1.0 (+ 1.0 x)) 3)) (/ x (+ 1.0 x)))
69.0ms	(pow (/ 1.0 (+ 1.0 x)) 3)

simplify3.0s

Counts

181 → 181

Iterations

Useful iterations: 2 (808.0ms)

Iter	Nodes	Cost
0	231	3028
1	739	2451
2	4051	2241
done	5001	2241

prune541.0ms

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	13	18
1	15	18
done	15	18

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.1s	8027×	body	80	nan
614.0ms	8000×	body	80	valid