Details

sample49.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
8.0ms	251×	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

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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:

9.0ms

(/ a (- (acos a)))

series31.0ms

Counts

1 → 3

Calls

1 calls:

31.0ms

(/ a (- (acos a)))

simplify4.6s

Counts

58 → 58

Iterations

Useful iterations: 5 (1.8s)

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

prune179.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite75.0ms

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:

33.0ms	(/ 1 (/ (acos a) (- a)))
17.0ms	(/ (acos a) (- a))

series107.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ 1 (/ (acos a) (- a)))
57.0ms	(/ (acos a) (- a))

simplify2.4s

Counts

222 → 222

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	293	3186
1	611	2657
2	1141	2356
3	2749	2260
done	5000	2260

prune490.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (asin a) (- a))
0.0b	(- (/ PI (* -2 a)) (/ (asin a) (- a)))
0.2b	(/ 1 (- (/ PI (* -2 a)) (/ (asin a) (- a))))
0.3b	(/ PI (* -2 a))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
56×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
17×	`associate-/r*`
15×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`difference-of-squares`
9×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1` `div-exp` `distribute-lft-out--`
4×	`cbrt-undiv` `neg-mul-1`
3×	`frac-2neg` `clear-num` `associate-/r/` `div-inv`
2×	`asin-acos` `flip3--` `div-sub` `frac-sub` `flip--`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `prod-exp` `cbrt-unprod` `inv-pow` `associate--r-`

Counts

4 → 140

Calls

4 calls:

16.0ms	(/ (asin a) (- a))
57.0ms	(- (/ PI (* -2 a)) (/ (asin a) (- a)))
103.0ms	(/ 1 (- (/ PI (* -2 a)) (/ (asin a) (- a))))
9.0ms	(/ PI (* -2 a))

series384.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (asin a) (- a))
105.0ms	(- (/ PI (* -2 a)) (/ (asin a) (- a)))
156.0ms	(/ 1 (- (/ PI (* -2 a)) (/ (asin a) (- a))))
74.0ms	(/ PI (* -2 a))

simplify2.9s

Counts

152 → 152

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	236	2145
1	465	1994
2	1091	1889
3	3338	1879
done	5000	1877

prune375.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ (acos a) (- a))) (cbrt (/ (acos a) (- a))))
0.5b	(cbrt (/ (acos a) (- a)))
0.5b	(cbrt (/ (acos a) (- a)))
0.5b	(cbrt (/ (acos a) (- a)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

262×	`cbrt-prod`
228×	`times-frac`
176×	`add-sqr-sqrt`
164×	`*-un-lft-identity`
152×	`add-cube-cbrt`
69×	`distribute-rgt-neg-in`
63×	`distribute-lft-neg-in`
43×	`swap-sqr`
37×	`associate-r` `associate-l`
21×	`neg-mul-1`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 276

Calls

4 calls:

82.0ms	(* (cbrt (/ (acos a) (- a))) (cbrt (/ (acos a) (- a))))
5.0ms	(cbrt (/ (acos a) (- a)))
8.0ms	(cbrt (/ (acos a) (- a)))
5.0ms	(cbrt (/ (acos a) (- a)))

series620.0ms

Calls

3 calls:

206.0ms	(cbrt (/ (acos a) (- a)))
205.0ms	(cbrt (/ (acos a) (- a)))
208.0ms	(cbrt (/ (acos a) (- a)))