Details

sample35.0ms

Algorithm

intervals

Results

9.0ms	278×	body	80	nan
9.0ms	256×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	122
1	7	122
2	11	122
done	11	122

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip--` `add-log-exp` `difference-of-squares`

Counts

1 → 16

Calls

1 calls:

4.0ms

(sqrt (- 1.0 (* x x)))

series374.0ms

Counts

1 → 3

Calls

1 calls:

374.0ms

(sqrt (- 1.0 (* x x)))

simplify1.8s

Counts

19 → 19

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	67	6209
1	154	4792
2	446	4430
3	1809	4430
done	5011	4390

prune78.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`sqrt-div`
13×	`flip3--` `flip--`
10×	`pow1`
9×	`sqrt-prod`
8×	`frac-times` `cbrt-div`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`add-cbrt-cube` `add-exp-log`
4×	`associate-r` `associate-l/` `associate-r/`
3×	`sqrt-pow1` `pow1/2` `add-log-exp` `difference-of-squares`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-plus` `cube-unmult` `pow-prod-up` `unswap-sqr`
1×	`cbrt-prod` `rem-sqrt-square` `pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod`

Counts

3 → 75

Calls

3 calls:

4.0ms	(sqrt (- 1.0 (* x x)))
38.0ms	(* (sqrt (- 1.0 (* x x))) (- 1.0 (* x x)))
9.0ms	(cbrt (* (sqrt (- 1.0 (* x x))) (- 1.0 (* x x))))

series299.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(sqrt (- 1.0 (* x x)))
136.0ms	(* (sqrt (- 1.0 (* x x))) (- 1.0 (* x x)))
85.0ms	(cbrt (* (sqrt (- 1.0 (* x x))) (- 1.0 (* x x))))

simplify2.9s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	146	33186
1	356	26634
2	1023	25468
3	3551	24068
done	5054	24068

prune423.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite446.0ms

Algorithm

rewrite-expression-head

Rules

684×	`sqrt-div`
280×	`frac-times`
228×	`flip3--` `flip--`
195×	`pow1`
168×	`sqrt-pow1`
136×	`pow-prod-up`
112×	`pow1/2`
92×	`associate-l/` `associate-r/`
80×	`cbrt-div`
78×	`add-sqr-sqrt`
66×	`sqrt-prod`
61×	`pow-prod-down`
38×	`pow-plus`
36×	`cube-unmult`
22×	`pow-sqr`
21×	`associate-l`
20×	`add-cbrt-cube` `add-exp-log`
15×	`associate-r`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`unswap-sqr`
10×	`prod-exp` `cbrt-unprod`
7×	`sqrt-unprod`
4×	`rem-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`*-commutative`
1×	`cbrt-prod` `pow2` `rem-square-sqrt` `pow1/3` `swap-sqr`

Counts

4 → 395

Calls

4 calls:

185.0ms	(* (* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x)))) (* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x)))))
127.0ms	(cbrt (* (* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x)))) (* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x))))))
52.0ms	(* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x))))
33.0ms	(* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x)))) (* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x)))))
76.0ms	(cbrt (* (* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x)))) (* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x))))))
354.0ms	(* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x))))
407.0ms	(* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x))))

simplify6.2s

Counts

407 → 407

Iterations

Useful iterations: done (6.1s)

Iter	Nodes	Cost
0	530	274883
1	1327	215318
2	3300	197234
done	5002	189194

prune1.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes87.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	322
1	10	322
done	10	322

end0.0ms

sample879.0ms

Algorithm

intervals

Results

397.0ms	8000×	body	80	valid
222.0ms	8008×	body	80	nan