Details

sample18.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
3.0ms	234×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	4	5
done	4	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize4.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ a (- (acos a)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

30×	`times-frac`
24×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-/r*`
4×	`neg-mul-1`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 57

Calls

1 calls:

4.0ms

(/ a (- (acos a)))

series30.0ms

Counts

1 → 3

Calls

1 calls:

30.0ms

(/ a (- (acos a)))

simplify2.6s

Counts

60 → 60

Iterations

Useful iterations: 4 (878.0ms)

Iter	Nodes	Cost
0	96	613
1	169	581
2	480	561
3	1406	557
4	3300	556
done	5001	556

prune123.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- (acos a)) a)
0.3b	(/ 1 (/ (- (acos a)) a))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

252×	`times-frac`
140×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
37×	`associate-/r*`
16×	`neg-mul-1`
15×	`add-exp-log`
13×	`associate-/l*`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv`
4×	`cbrt-undiv`
3×	`pow1`
2×	`expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`neg-sub0` `pow-flip` `div-sub` `distribute-frac-neg` `associate-/r/` `inv-pow`

Counts

2 → 221

Calls

2 calls:

4.0ms	(/ (- (acos a)) a)
14.0ms	(/ 1 (/ (- (acos a)) a))

series62.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (- (acos a)) a)
26.0ms	(/ 1 (/ (- (acos a)) a))

simplify1.9s

Counts

227 → 227

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	292	3194
1	674	2774
2	2302	2325
done	5000	2314

prune297.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ 1 (* (- (acos a)) (/ 1 a)))
0.3b	(* (- (acos a)) (/ 1 a))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log`
21×	`add-sqr-sqrt`
18×	`div-exp`
16×	`prod-exp` `add-cbrt-cube`
15×	`*-un-lft-identity`
14×	`add-cube-cbrt` `times-frac`
13×	`associate-r`
10×	`associate-l`
9×	`rec-exp` `1-exp`
7×	`pow1`
5×	`cbrt-undiv`
4×	`cbrt-unprod`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-/l*` `unswap-sqr`
2×	`expm1-log1p-u` `pow-flip` `associate-*r/` `pow-prod-down` `associate-/r/` `un-div-inv` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`distribute-lft-neg-out` `neg-mul-1` `frac-2neg` `clear-num` `associate-/r` `-commutative` `inv-pow`

Counts

2 → 88

Calls

2 calls:

10.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
12.0ms	(* (- (acos a)) (/ 1 a))

series65.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
39.0ms	(* (- (acos a)) (/ 1 a))

simplify3.7s

Counts

94 → 94

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	129	968
1	363	741
2	1294	559
3	3276	553
done	5000	553

prune130.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt a)
0.7b	(cbrt a)
1.0b	(sqrt (acos a))
1.0b	(sqrt (acos a))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

0.0ms	(cbrt a)
0.0ms	(cbrt a)
1.0ms	(sqrt (acos a))
1.0ms	(sqrt (acos a))

series397.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(cbrt a)
184.0ms	(cbrt a)
10.0ms	(sqrt (acos a))
11.0ms	(sqrt (acos a))

simplify2.2s

Counts

68 → 68

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	44	312
1	64	280
2	110	266
3	227	260
4	635	260
5	3278	260
done	5000	260

prune166.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
done	4	5

end0.0ms

sample448.0ms

Algorithm

intervals

Results

165.0ms	8000×	body	80	valid
106.0ms	8035×	body	80	nan