Details

sample21.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
4.0ms	218×	body	80	nan

simplify1.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
done	4	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

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` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 55

Calls

1 calls:

7.0ms

(/ a (- (acos a)))

series27.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(/ a (- (acos a)))

simplify4.9s

Counts

58 → 58

Iterations

Useful iterations: 5 (1.9s)

Iter	Nodes	Cost
0	94	601
1	164	569
2	334	551
3	587	551
4	1101	551
5	2149	546
done	5000	546

prune112.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite47.0ms

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`
44×	`associate-/r*`
16×	`neg-mul-1`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv`
3×	`pow1`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`acos-asin` `pow-flip` `div-sub` `associate-/r/` `inv-pow`

Counts

2 → 216

Calls

2 calls:

8.0ms	(/ (acos a) (- a))
16.0ms	(/ 1 (/ (acos a) (- a)))

series96.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (acos a) (- a))
51.0ms	(/ 1 (/ (acos a) (- a)))

simplify2.4s

Counts

222 → 222

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	293	3186
1	611	2657
2	1135	2356
3	2752	2260
done	5000	2260

prune374.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
16×	`add-cube-cbrt`
12×	`add-exp-log`
10×	`add-cbrt-cube` `difference-of-squares`
7×	`associate-/r*`
6×	`associate-/l*`
5×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `div-exp`
3×	`cbrt-undiv` `associate-/r/`
2×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv`
1×	`sub-neg` `rec-exp` `asin-acos` `pow-flip` `diff-log` `1-exp` `div-sub` `prod-exp` `cbrt-unprod` `inv-pow` `associate--r-`

Counts

3 → 84

Calls

3 calls:

52.0ms	(- (/ PI (* a -2)) (/ (asin a) (- a)))
8.0ms	(/ PI (* a -2))
70.0ms	(/ 1 (- (/ PI (* a -2)) (/ (asin a) (- a))))

series279.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(- (/ PI (* a -2)) (/ (asin a) (- a)))
39.0ms	(/ PI (* a -2))
125.0ms	(/ 1 (- (/ PI (* a -2)) (/ (asin a) (- a))))

simplify2.1s

Counts

93 → 93

Iterations

Useful iterations: 3 (828.0ms)

Iter	Nodes	Cost
0	154	1530
1	326	1423
2	762	1330
3	2349	1320
done	5000	1320

prune260.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))) (cbrt (- (/ PI (* a -2)) (/ (asin a) (- a)))))
0.5b	(cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))
0.5b	(cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))
0.5b	(cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))

rewrite480.0ms

Algorithm

rewrite-expression-head

Rules

644×	`times-frac`
577×	`add-sqr-sqrt`
408×	`cbrt-prod`
373×	`*-un-lft-identity`
237×	`add-cube-cbrt`
136×	`difference-of-squares`
68×	`distribute-lft-out--`
42×	`cbrt-div`
34×	`associate-/l*`
33×	`associate-/r/`
14×	`flip3--` `frac-sub` `flip--`
13×	`add-exp-log`
11×	`div-inv`
9×	`associate-/r*`
7×	`pow1`
6×	`div-exp` `add-cbrt-cube`
5×	`pow1/3`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-div`
2×	`pow-flip`
1×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/` `inv-pow`

Counts

4 → 423

Calls

4 calls:

261.0ms	(/ (/ 1 (cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))) (cbrt (- (/ PI (* a -2)) (/ (asin a) (- a)))))
59.0ms	(cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))
44.0ms	(cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))
37.0ms	(cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))

series1.5s

Counts

4 → 12

Calls

4 calls:

439.0ms	(/ (/ 1 (cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))) (cbrt (- (/ PI (* a -2)) (/ (asin a) (- a)))))
336.0ms	(cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))
408.0ms	(cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))
362.0ms	(cbrt (- (/ PI (* a -2)) (/ (asin a) (- a))))

simplify3.1s

Counts

435 → 435

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	566	21415
1	1275	20223
2	1890	19858
3	4040	19319
done	5000	17563

prune1.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes78.0ms

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

sample1.5s

Algorithm

intervals

Results

652.0ms	8039×	body	80	nan
392.0ms	8000×	body	80	valid