Details

sample272.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
7.0ms	232×	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

prune4.0ms

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

rewrite28.0ms

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))))
11.0ms	(/ (- 1.0 x) (+ 1.0 x))
12.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

series144.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
32.0ms	(/ (- 1.0 x) (+ 1.0 x))
109.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify928.0ms

Counts

100 → 100

Iterations

Useful iterations: 3 (440.0ms)

Iter	Nodes	Cost
0	167	1451
1	352	1376
2	849	1284
3	2267	1268
done	5000	1268

prune204.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

254×	`sqrt-prod`
209×	`add-sqr-sqrt`
190×	`*-un-lft-identity`
177×	`times-frac`
92×	`add-cube-cbrt`
44×	`associate-r`
30×	`associate-l`
24×	`unswap-sqr`
23×	`distribute-lft-out`
22×	`distribute-lft-out--` `difference-of-squares`
15×	`sqrt-div`
14×	`associate-/r*`
12×	`add-exp-log`
11×	`pow1`
10×	`associate-/r/` `add-cbrt-cube`
8×	`associate-/l*`
5×	`flip3-+` `flip-+` `div-inv`
4×	`sqrt-pow1` `pow1/2` `add-log-exp`
3×	`rem-sqrt-square` `pow-flip` `div-exp` `pow-prod-down`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `rec-exp` `flip3--` `sqrt-unprod` `1-exp` `div-sub` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `inv-pow`

Counts

4 → 284

Calls

4 calls:

12.0ms	(sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
70.0ms	(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
9.0ms	(/ 1 (sqrt (+ 1.0 x)))
12.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
88.0ms	(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
54.0ms	(/ 1 (sqrt (+ 1.0 x)))
91.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify768.0ms

Counts

296 → 296

Iterations

Useful iterations: done (759.0ms)

Iter	Nodes	Cost
0	395	5645
1	857	5136
2	2248	4935
done	5001	4909

prune616.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes69.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	20
1	19	20
done	19	20

end0.0ms

sample680.0ms

Algorithm

intervals

Results

296.0ms	8000×	body	80	valid
200.0ms	8120×	body	80	nan