Details

sample122.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
18.0ms	262×	body	80	nan

simplify74.0ms

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

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(atan (sqrt (/ (- 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×	`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 → 91

Calls

3 calls:

32.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
24.0ms	(/ (- 1.0 x) (+ 1.0 x))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series186.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
40.0ms	(/ (- 1.0 x) (+ 1.0 x))
29.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify1.6s

Counts

100 → 100

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	167	1451
1	356	1376
2	865	1284
3	2147	1268
done	5000	1252

prune333.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

322×	`times-frac`
289×	`*-un-lft-identity`
214×	`add-sqr-sqrt`
139×	`add-cube-cbrt`
83×	`sqrt-prod`
41×	`distribute-lft-out`
33×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-/r*`
18×	`associate-/r/`
17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`div-inv`
8×	`flip3--` `div-exp` `flip--`
7×	`pow1` `associate-/l*`
5×	`rem-sqrt-square`
4×	`cbrt-undiv` `add-log-exp`
3×	`sqrt-pow1`
2×	`rec-exp` `pow-flip` `frac-2neg` `1-exp` `clear-num` `associate-/l/` `inv-pow`
1×	`flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 280

Calls

4 calls:

59.0ms	(sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x))))
1.0ms	(atan (sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x)))))
27.0ms	(/ (+ 1.0 x) (- 1.0 x))
43.0ms	(/ 1 (/ (+ 1.0 x) (- 1.0 x)))

series651.0ms

Counts

4 → 12

Calls

4 calls:

538.0ms	(sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x))))
4.0ms	(atan (sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x)))))
58.0ms	(/ (+ 1.0 x) (- 1.0 x))
49.0ms	(/ 1 (/ (+ 1.0 x) (- 1.0 x)))

simplify3.1s

Counts

292 → 292

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	368	5447
1	698	4596
2	1521	4100
3	3933	3860
done	5000	3830

prune641.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite543.0ms

Algorithm

rewrite-expression-head

Rules

317×	`add-sqr-sqrt`
278×	`*-un-lft-identity`
225×	`times-frac`
144×	`difference-of-squares`
109×	`associate-l`
108×	`unpow-prod-down` `cube-prod`
82×	`add-cube-cbrt`
72×	`sqr-pow`
52×	`distribute-lft-out`
45×	`distribute-lft-out--`
34×	`add-exp-log`
28×	`associate-/l*`
22×	`add-cbrt-cube`
19×	`associate-r`
11×	`div-exp`
9×	`pow1` `difference-cubes` `prod-exp`
8×	`associate-/r/`
7×	`associate-/r*` `unswap-sqr`
6×	`cbrt-undiv`
5×	`flip3-+` `cbrt-unprod` `flip-+`
4×	`div-inv` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-*r/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/`
1×	`distribute-rgt-in` `frac-times` `flip3--` `pow-flip` `distribute-lft-in` `div-sub` `associate-*l/` `un-div-inv` `flip--` `inv-pow`

Counts

4 → 354

Calls

4 calls:

41.0ms	(* x (+ x 1.0))
119.0ms	(/ (- (pow 1.0 3) (pow x 3)) (+ x 1.0))
288.0ms	(* (/ (- (pow 1.0 3) (pow x 3)) (+ x 1.0)) (/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0))))
44.0ms	(/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* x (+ x 1.0))
53.0ms	(/ (- (pow 1.0 3) (pow x 3)) (+ x 1.0))
94.0ms	(* (/ (- (pow 1.0 3) (pow x 3)) (+ x 1.0)) (/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0))))
103.0ms	(/ 1 (+ (* x (+ x 1.0)) (* 1.0 1.0)))

simplify2.8s

Counts

366 → 366

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	368	8243
1	1039	7635
2	2985	7115
done	5001	7115

prune1.4s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	27
1	25	27
done	25	27

end0.0ms

sample1.5s

Algorithm

intervals

Results

615.0ms	8000×	body	80	valid
614.0ms	7984×	body	80	nan