Details

sample158.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
16.0ms	230×	body	80	nan

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

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))

rewrite77.0ms

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))))
29.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
40.0ms	(/ (- 1.0 x) (+ 1.0 x))

series235.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
146.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
84.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify1.4s

Counts

106 → 106

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	168	1479
1	370	1398
2	1473	1313
done	5001	1311

prune367.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize29.0ms

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)))

rewrite524.0ms

Algorithm

rewrite-expression-head

Rules

609×	`*-un-lft-identity`
500×	`times-frac`
348×	`add-sqr-sqrt`
324×	`prod-diff`
323×	`add-cube-cbrt`
127×	`distribute-lft-out`
86×	`associate-/r/`
43×	`flip3-+` `flip-+` `div-inv`
18×	`fma-neg`
17×	`sqrt-prod`
14×	`distribute-lft-out--`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `difference-of-squares`
6×	`distribute-rgt-out--` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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 → 475

Calls

4 calls:

236.0ms	(sqrt (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x))))
25.0ms	(/ x (+ 1.0 x))
12.0ms	(/ 1.0 (+ 1.0 x))
164.0ms	(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(sqrt (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x))))
36.0ms	(/ x (+ 1.0 x))
47.0ms	(/ 1.0 (+ 1.0 x))
100.0ms	(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))

simplify2.8s

Counts

487 → 487

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	505	21239
1	1168	18727
2	4285	14555
done	5000	14555

prune1.5s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

286.0ms	(cbrt x)
275.0ms	(cbrt x)
268.0ms	(cbrt x)
315.0ms	(cbrt x)

simplify1.2s

Counts

64 → 64

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	26	284
1	47	268
2	115	244
3	334	232
4	1002	232
done	5001	232

prune664.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify20.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	69
1	40	69
2	44	69
3	46	69
done	46	69

end0.0ms

sample2.0s

Algorithm

intervals

Results

907.0ms	8027×	body	80	nan
728.0ms	8000×	body	80	valid