Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
4.0ms	259×	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: 0.2b

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b	(/ 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` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 55

Calls

1 calls:

4.0ms

(/ a (- (acos a)))

series24.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

(/ a (- (acos a)))

simplify2.8s

Counts

58 → 58

Iterations

Useful iterations: 5 (1.2s)

Iter	Nodes	Cost
0	94	601
1	164	569
2	328	551
3	713	551
4	1237	551
5	2175	546
done	5001	546

prune110.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

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` `frac-2neg` `clear-num` `add-log-exp`
1×	`acos-asin` `rec-exp` `pow-flip` `1-exp` `div-sub` `associate-/r/` `distribute-neg-frac` `inv-pow`

Counts

2 → 168

Calls

2 calls:

2.0ms	(/ (acos a) a)
10.0ms	(/ 1 (- (/ (acos a) a)))

series56.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ (acos a) a)
24.0ms	(/ 1 (- (/ (acos a) a)))

simplify3.5s

Counts

174 → 174

Iterations

Useful iterations: 3 (568.0ms)

Iter	Nodes	Cost
0	261	2383
1	483	1978
2	785	1835
3	1708	1689
4	3454	1689
done	5001	1689

prune218.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (acos a))
0.3b	(/ (/ 1 (acos a)) (- (/ 1 a)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

930×	`times-frac`
437×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
182×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
61×	`div-inv`
33×	`associate-/r*`
16×	`associate-/l*`
15×	`add-exp-log`
14×	`neg-mul-1`
9×	`add-cbrt-cube`
8×	`div-exp`
4×	`cbrt-undiv`
3×	`pow1`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`pow-flip` `associate-/r/` `associate-/l/` `distribute-neg-frac` `inv-pow`

Counts

2 → 482

Calls

2 calls:

2.0ms	(/ 1 (acos a))
20.0ms	(/ (/ 1 (acos a)) (- (/ 1 a)))

series29.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ 1 (acos a))
24.0ms	(/ (/ 1 (acos a)) (- (/ 1 a)))

simplify2.0s

Counts

488 → 488

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	709	10289
1	1828	7575
2	2998	6656
done	5001	6638

prune324.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

29×	`times-frac`
28×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`add-cube-cbrt`
15×	`add-exp-log`
13×	`associate-r`
9×	`add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1`
4×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `div-exp` `prod-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-*r/` `associate-/r/` `un-div-inv` `cbrt-unprod` `div-inv` `distribute-neg-frac` `add-log-exp`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `inv-pow`

Counts

2 → 81

Calls

2 calls:

4.0ms	(/ 1 (- (* (acos a) (/ 1 a))))
8.0ms	(* (acos a) (/ 1 a))

series55.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(/ 1 (- (* (acos a) (/ 1 a))))
30.0ms	(* (acos a) (/ 1 a))

simplify3.4s

Counts

87 → 87

Iterations

Useful iterations: 3 (953.0ms)

Iter	Nodes	Cost
0	134	955
1	293	674
2	658	593
3	2316	559
done	5000	559

prune120.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes47.0ms

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

sample444.0ms

Algorithm

intervals

Results

161.0ms	8000×	body	80	valid
107.0ms	8082×	body	80	nan