Details

sample81.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
11.0ms	288×	body	80	nan

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 3 expressions with local error:

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

rewrite189.0ms

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))))
92.0ms	(/ (- 1.0 x) (+ 1.0 x))
84.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

series197.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
52.0ms	(/ (- 1.0 x) (+ 1.0 x))
137.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify1.9s

Counts

100 → 100

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	167	1451
1	356	1376
2	866	1284
3	2144	1268
done	5000	1252

prune321.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ 1.0 x))
0.0b	(atan (sqrt (* (/ 1 (+ 1.0 x)) (- 1.0 x))))
0.0b	(* (/ 1 (+ 1.0 x)) (- 1.0 x))
0.0b	(sqrt (* (/ 1 (+ 1.0 x)) (- 1.0 x)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
18×	`associate-l`
17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`pow1`
7×	`distribute-lft-out`
5×	`sqrt-div` `associate-r`
4×	`frac-times` `flip3--` `associate-r/` `div-exp` `prod-exp` `associate-/r` `associate-/r/` `flip--` `add-log-exp`
3×	`associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `rec-exp` `distribute-lft-in` `sqrt-pow1` `flip3-+` `1-exp` `pow-prod-down` `associate-*l/` `cbrt-unprod` `flip-+` `div-inv`
1×	`pow-flip` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `*-commutative` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 110

Calls

4 calls:

12.0ms	(/ 1 (+ 1.0 x))
1.0ms	(atan (sqrt (* (/ 1 (+ 1.0 x)) (- 1.0 x))))
99.0ms	(* (/ 1 (+ 1.0 x)) (- 1.0 x))
29.0ms	(sqrt (* (/ 1 (+ 1.0 x)) (- 1.0 x)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (+ 1.0 x))
4.0ms	(atan (sqrt (* (/ 1 (+ 1.0 x)) (- 1.0 x))))
55.0ms	(* (/ 1 (+ 1.0 x)) (- 1.0 x))
127.0ms	(sqrt (* (/ 1 (+ 1.0 x)) (- 1.0 x)))

simplify2.7s

Counts

122 → 122

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	192	1536
1	445	1302
2	1232	1158
3	3276	1125
done	5001	1125

prune375.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	16	13
done	16	13

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
495.0ms	8037×	body	80	nan