Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
3.0ms	228×	body	80	nan

simplify1.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
done	4	5

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize4.0ms

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)))

simplify3.2s

Counts

58 → 58

Iterations

Useful iterations: 5 (1.2s)

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

prune100.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

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:

15.0ms	(/ 1 (/ (acos a) (- a)))
10.0ms	(/ (acos a) (- a))

series58.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ 1 (/ (acos a) (- a)))
31.0ms	(/ (acos a) (- a))

simplify1.5s

Counts

222 → 222

Iterations

Useful iterations: 3 (816.0ms)

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

prune250.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (* (acos a) (/ -1 a)))
0.4b	(* (acos a) (/ -1 a))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
13×	`times-frac` `associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`div-exp`
8×	`prod-exp`
7×	`pow1`
5×	`cbrt-undiv`
4×	`cbrt-unprod`
3×	`rec-exp` `1-exp` `associate-l` `associate-/l*`
2×	`pow-flip` `associate-*r/` `pow-prod-down` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r` `associate-/r/` `-commutative` `inv-pow`

Counts

2 → 65

Calls

2 calls:

16.0ms	(/ 1 (* (acos a) (/ -1 a)))
13.0ms	(* (acos a) (/ -1 a))

series56.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(/ 1 (* (acos a) (/ -1 a)))
34.0ms	(* (acos a) (/ -1 a))

simplify3.2s

Counts

71 → 71

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	111	695
1	259	569
2	859	446
3	4033	444
done	5000	444

prune107.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

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:

4.0ms	(cbrt (/ (acos a) (- a)))
4.0ms	(cbrt (/ (acos a) (- a)))
4.0ms	(cbrt (/ (acos a) (- a)))
60.0ms	(* (cbrt (/ (acos a) (- a))) (cbrt (/ (acos a) (- a))))

series673.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (/ (acos a) (- a)))
159.0ms	(cbrt (/ (acos a) (- a)))
150.0ms	(cbrt (/ (acos a) (- a)))
208.0ms	(* (cbrt (/ (acos a) (- a))) (cbrt (/ (acos a) (- a))))

simplify2.7s

Counts

288 → 288

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	297	4926
1	459	4666
2	1205	4571
3	2040	4429
4	4839	4176
done	5000	4060

prune735.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes73.0ms

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

sample503.0ms

Algorithm

intervals

Results

159.0ms	8000×	body	80	valid
104.0ms	7863×	body	80	nan