Details

sample275.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	259×	body	80	nan

simplify16.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))

rewrite27.0ms

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:

0.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
13.0ms	(/ (- 1.0 x) (+ 1.0 x))

series147.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
92.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
51.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify1.1s

Counts

100 → 100

Iterations

Useful iterations: 3 (467.0ms)

Iter	Nodes	Cost
0	167	1451
1	352	1376
2	845	1324
3	2257	1268
done	5001	1268

prune215.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
78×	`*-un-lft-identity`
60×	`add-sqr-sqrt`
56×	`times-frac`
40×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`sqrt-div` `associate-/l*`
7×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 128

Calls

4 calls:

0.0ms	(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
15.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
4.0ms	(sqrt (+ 1.0 x))
4.0ms	(sqrt (- 1.0 x))

series162.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
97.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
30.0ms	(sqrt (+ 1.0 x))
32.0ms	(sqrt (- 1.0 x))

simplify1.0s

Counts

140 → 140

Iterations

Useful iterations: 3 (427.0ms)

Iter	Nodes	Cost
0	189	2206
1	353	1977
2	831	1899
3	2233	1866
done	5000	1866

prune291.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

111×	`sqrt-prod`
58×	`add-sqr-sqrt`
41×	`*-un-lft-identity` `sqrt-pow1`
34×	`sqrt-div`
32×	`pow1`
21×	`add-cube-cbrt` `pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+` `distribute-lft-out`
6×	`add-exp-log` `add-cbrt-cube`
5×	`rem-sqrt-square` `pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `flip3--` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 149

Calls

4 calls:

3.0ms	(sqrt (- 1.0 x))
4.0ms	(sqrt (sqrt (+ 1.0 x)))
4.0ms	(sqrt (sqrt (+ 1.0 x)))
26.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (- 1.0 x))
87.0ms	(sqrt (sqrt (+ 1.0 x)))
89.0ms	(sqrt (sqrt (+ 1.0 x)))
37.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify1.4s

Counts

161 → 161

Iterations

Useful iterations: 3 (653.0ms)

Iter	Nodes	Cost
0	190	2268
1	373	1461
2	976	1389
3	2970	1326
done	5001	1326

prune344.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample704.0ms

Algorithm

intervals

Results

307.0ms	8000×	body	80	valid
205.0ms	8082×	body	80	nan