Details

sample320.0ms

Algorithm

intervals

Results

107.0ms	248×	body	80	nan
29.0ms	256×	body	80	valid

simplify123.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite58.0ms

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-cbrt-cube` `add-exp-log` `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` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `div-exp` `flip--`

Counts

3 → 91

Calls

3 calls:

20.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
24.0ms	(/ (- 1.0 x) (+ 1.0 x))

series259.0ms

Counts

3 → 9

Calls

3 calls:

200.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
4.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
55.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify865.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	1408
1	354
0	162

prune466.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))))
0.0b	(cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))
0.0b	(/ (- 1.0 x) (+ x 1.0))
0.0b	(pow (/ (- 1.0 x) (+ x 1.0)) 3)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
100×	`times-frac`
99×	`add-sqr-sqrt`
58×	`cbrt-prod`
57×	`add-cube-cbrt`
52×	`unpow-prod-down` `cube-prod`
26×	`distribute-lft-out`
21×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `flip3-+` `flip-+` `div-inv` `associate-/l*`
4×	`associate-/r*` `add-log-exp`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `cbrt-undiv` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow` `associate-/l/`
1×	`pow-to-exp` `cbrt-div` `clear-num` `pow-pow` `frac-2neg` `flip3--` `pow1/3` `div-sub` `rem-cbrt-cube` `flip--`

Counts

4 → 193

Calls

4 calls:

1.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))))
19.0ms	(cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))
23.0ms	(/ (- 1.0 x) (+ x 1.0))
33.0ms	(pow (/ (- 1.0 x) (+ x 1.0)) 3)

series191.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))))
58.0ms	(cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))
46.0ms	(/ (- 1.0 x) (+ x 1.0))
82.0ms	(pow (/ (- 1.0 x) (+ x 1.0)) 3)

simplify1.7s

Counts

205 → 205

Iterations

Iter	Nodes
done	5000
2	4132
1	735
0	211

prune647.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(* (- 1.0 x) (/ 1 (+ x 1.0)))
0.0b	(cbrt (pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3))
0.0b	(pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3)

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
27×	`add-exp-log`
26×	`times-frac`
24×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-cbrt-cube`
12×	`cube-div`
10×	`pow1`
8×	`cbrt-prod` `prod-exp`
7×	`distribute-lft-out`
6×	`frac-times` `cbrt-div` `flip3--` `div-exp` `associate-*l/` `flip--`
5×	`associate-l` `pow-exp`
4×	`associate-/r*` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `pow-unpow` `1-exp` `associate-r/` `un-div-inv` `associate-/l` `rem-cube-cbrt` `unswap-sqr`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `flip3-+` `unpow3` `cube-prod` `pow-prod-down` `flip-+` `div-inv` `sqr-pow`
1×	`pow-to-exp` `clear-num` `frac-2neg` `pow1/3` `*-commutative` `rem-cbrt-cube` `pow-flip` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 139

Calls

4 calls:

19.0ms	(/ 1 (+ x 1.0))
54.0ms	(* (- 1.0 x) (/ 1 (+ x 1.0)))
4.0ms	(cbrt (pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3))
28.0ms	(pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3)

series226.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1 (+ x 1.0))
59.0ms	(* (- 1.0 x) (/ 1 (+ x 1.0)))
35.0ms	(cbrt (pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3))
88.0ms	(pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3)

simplify1.9s

Counts

151 → 151

Iterations

Iter	Nodes
done	5001
2	3587
1	596
0	200

prune688.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	14

end0.0ms

sample2.0s

Algorithm

intervals

Results

892.0ms	7876×	body	80	nan
744.0ms	8000×	body	80	valid