Details

sample123.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
19.0ms	243×	body	80	nan

simplify78.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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))

rewrite68.0ms

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

series188.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
130.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
50.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify1.1s

Counts

106 → 106

Iterations

Useful iterations: done (1.1s)

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

prune456.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

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` `expm1-log1p-u` `associate-/l*`
4×	`associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `log1p-expm1` `div-exp` `clear-num` `flip--` `expm1-udef`

Counts

4 → 110

Calls

4 calls:

27.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(log1p (sqrt (/ (- 1.0 x) (+ 1.0 x))))
1.0ms	(expm1 (log1p (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
50.0ms	(/ (- 1.0 x) (+ 1.0 x))

series1.1s

Counts

4 → 12

Calls

4 calls:

126.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
361.0ms	(log1p (sqrt (/ (- 1.0 x) (+ 1.0 x))))
572.0ms	(expm1 (log1p (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
53.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify1.6s

Counts

122 → 122

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	218	1879
1	518	1750
2	2380	1616
done	5000	1606

prune456.0ms

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

sample2.1s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
579.0ms	7917×	body	80	nan