Details

sample40.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
9.0ms	270×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
done	4	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite20.0ms

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:

16.0ms

(/ a (- (acos a)))

series49.0ms

Counts

1 → 3

Calls

1 calls:

49.0ms

(/ a (- (acos a)))

simplify4.9s

Counts

60 → 60

Iterations

Useful iterations: 5 (2.0s)

Iter	Nodes	Cost
0	96	613
1	166	581
2	333	563
3	587	563
4	1105	563
5	2150	558
done	5001	558

prune176.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

171×	`times-frac`
101×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
52×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
33×	`associate-/r*`
10×	`div-inv`
8×	`add-exp-log`
6×	`add-cbrt-cube` `associate-/l*`
4×	`neg-mul-1`
3×	`pow1` `div-exp`
2×	`cbrt-undiv` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `rec-exp` `pow-flip` `1-exp` `div-sub` `associate-/r/` `distribute-neg-frac` `inv-pow`

Counts

2 → 172

Calls

2 calls:

31.0ms	(/ 1 (- (/ (acos a) a)))
11.0ms	(/ (acos a) a)

series94.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ 1 (- (/ (acos a) a)))
49.0ms	(/ (acos a) a)

simplify6.4s

Counts

178 → 178

Iterations

Useful iterations: 3 (620.0ms)

Iter	Nodes	Cost
0	265	2409
1	472	2004
2	782	1861
3	1534	1711
4	2784	1711
done	5000	1711

prune370.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (/ PI 2) a) (/ (asin a) a))
0.0b	(/ (asin a) a)
0.3b	(/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))
0.3b	(/ (/ PI 2) a)

rewrite568.0ms

Algorithm

rewrite-expression-head

Rules

1626×	`times-frac`
1097×	`add-sqr-sqrt`
980×	`*-un-lft-identity`
908×	`add-cube-cbrt`
559×	`prod-diff`
124×	`div-inv`
56×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
54×	`difference-of-squares`
43×	`fma-neg`
38×	`associate-/r*`
36×	`distribute-lft-out--`
19×	`associate-/l*`
15×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`distribute-rgt-out--`
6×	`div-exp` `add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `neg-mul-1` `associate-/r/` `log1p-expm1-u` `distribute-neg-frac`
3×	`frac-2neg` `clear-num`
2×	`asin-acos` `flip3--` `div-sub` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `associate-/l/` `inv-pow` `associate--r-`

Counts

4 → 885

Calls

4 calls:

135.0ms	(- (/ (/ PI 2) a) (/ (asin a) a))
9.0ms	(/ (asin a) a)
271.0ms	(/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))
12.0ms	(/ (/ PI 2) a)

series409.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ (/ PI 2) a) (/ (asin a) a))
53.0ms	(/ (asin a) a)
181.0ms	(/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))
52.0ms	(/ (/ PI 2) a)

simplify3.2s

Counts

897 → 897

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	1070	36729
1	2160	32089
2	4188	24236
done	5000	24233

prune2.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (asin a) a)
0.0b	(- (* (/ PI 2) (/ 1 a)) (/ (asin a) a))
0.3b	(/ 1 (- (- (* (/ PI 2) (/ 1 a)) (/ (asin a) a))))
0.4b	(* (/ PI 2) (/ 1 a))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

79×	`times-frac`
75×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
58×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
15×	`associate-/r*`
14×	`div-inv`
13×	`associate-r` `associate-l` `prod-diff`
11×	`div-exp`
9×	`distribute-rgt-out--`
8×	`prod-exp` `associate-/r/` `frac-sub` `distribute-neg-frac`
7×	`pow1`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp` `unswap-sqr`
5×	`associate-*r/` `un-div-inv`
4×	`expm1-log1p-u` `neg-mul-1` `cbrt-unprod` `log1p-expm1-u` `sub-div`
3×	`frac-times` `rec-exp` `1-exp` `associate-*l/`
2×	`asin-acos` `flip3--` `frac-2neg` `div-sub` `clear-num` `flip--`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `pow-prod-down` `*-commutative` `inv-pow` `associate--r-`

Counts

4 → 202

Calls

4 calls:

6.0ms	(/ (asin a) a)
34.0ms	(- (* (/ PI 2) (/ 1 a)) (/ (asin a) a))
112.0ms	(/ 1 (- (- (* (/ PI 2) (/ 1 a)) (/ (asin a) a))))
44.0ms	(* (/ PI 2) (/ 1 a))

series525.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (asin a) a)
149.0ms	(- (* (/ PI 2) (/ 1 a)) (/ (asin a) a))
219.0ms	(/ 1 (- (- (* (/ PI 2) (/ 1 a)) (/ (asin a) a))))
84.0ms	(* (/ PI 2) (/ 1 a))

simplify2.2s

Counts

214 → 214

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	369	3676
1	849	3002
2	2163	2642
done	5000	2493

prune674.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes92.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
done	4	5

end0.0ms

sample1.1s

Algorithm

intervals

Results

357.0ms	8000×	body	80	valid
278.0ms	7844×	body	80	nan