Details

sample101.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
16.0ms	288×	body	80	nan

simplify72.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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)))

rewrite65.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 97

Calls

3 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
26.0ms	(/ (- 1.0 x) (+ 1.0 x))
28.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

series182.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
40.0ms	(/ (- 1.0 x) (+ 1.0 x))
138.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify2.1s

Counts

106 → 106

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	173	1505
1	372	1422
2	914	1333
3	2329	1320
done	5001	1300

prune322.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`pow1`
7×	`distribute-lft-out`
6×	`sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `flip3--` `div-exp` `associate-l/` `prod-exp` `associate-/r` `associate-/r/` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `flip3-+` `1-exp` `associate-*r/` `pow-prod-down` `un-div-inv` `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 → 116

Calls

4 calls:

12.0ms	(/ 1 (+ 1.0 x))
1.0ms	(atan (sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x)))))
26.0ms	(sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x))))
88.0ms	(* (- 1.0 x) (/ 1 (+ 1.0 x)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (+ 1.0 x))
5.0ms	(atan (sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x)))))
106.0ms	(sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x))))
49.0ms	(* (- 1.0 x) (/ 1 (+ 1.0 x)))

simplify3.8s

Counts

128 → 128

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	193	1579
1	441	1301
2	1268	1172
3	3915	1136
done	5000	1130

prune418.0ms

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	11	13
1	16	13
done	16	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

782.0ms	8000×	body	80	valid
495.0ms	8037×	body	80	nan