Details

sample97.0ms

Algorithm

intervals

Results

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

simplify56.0ms

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

localize15.0ms

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)))

rewrite62.0ms

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))))
25.0ms	(/ (- 1.0 x) (+ 1.0 x))
21.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

series322.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
141.0ms	(/ (- 1.0 x) (+ 1.0 x))
174.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify2.2s

Counts

106 → 106

Iterations

Useful iterations: done (2.2s)

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

prune323.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (expm1 (log1p (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
0.0b	(expm1 (log1p (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
46×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
25×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `expm1-log1p` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--` `expm1-udef`

Counts

4 → 108

Calls

4 calls:

1.0ms	(atan (expm1 (log1p (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
0.0ms	(expm1 (log1p (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
26.0ms	(/ (- 1.0 x) (+ 1.0 x))
23.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

series951.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan (expm1 (log1p (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
766.0ms	(expm1 (log1p (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
52.0ms	(/ (- 1.0 x) (+ 1.0 x))
127.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify1.6s

Counts

120 → 120

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	225	1895
1	522	1734
2	1486	1603
done	5001	1568

prune472.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.0s

Algorithm

intervals

Results

913.0ms	8037×	body	80	nan
805.0ms	8000×	body	80	valid