Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
5.0ms	270×	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)))

rewrite15.0ms

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:

10.0ms

(/ 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

prune174.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite52.0ms

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:

26.0ms	(/ 1 (- (/ (acos a) a)))
11.0ms	(/ (acos a) a)

series99.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ 1 (- (/ (acos a) a)))
56.0ms	(/ (acos a) a)

simplify6.2s

Counts

178 → 178

Iterations

Useful iterations: 3 (744.0ms)

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

prune333.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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)

rewrite515.0ms

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:

129.0ms	(- (/ (/ PI 2) a) (/ (asin a) a))
7.0ms	(/ (asin a) a)
222.0ms	(/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))
13.0ms	(/ (/ PI 2) a)

series439.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (/ (/ PI 2) a) (/ (asin a) a))
38.0ms	(/ (asin a) a)
206.0ms	(/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))
94.0ms	(/ (/ PI 2) a)

simplify3.0s

Counts

897 → 897

Iterations

Useful iterations: done (3.0s)

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

prune2.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ 1 (- (* (acos a) (/ 1 a))))
0.4b	(* (acos a) (/ 1 a))

rewrite28.0ms

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` `expm1-log1p-u` `rec-exp` `1-exp` `associate-*r/` `associate-/r/` `un-div-inv` `cbrt-unprod` `log1p-expm1-u` `div-inv` `distribute-neg-frac` `add-log-exp`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `inv-pow`

Counts

2 → 85

Calls

2 calls:

9.0ms	(/ 1 (- (* (acos a) (/ 1 a))))
16.0ms	(* (acos a) (/ 1 a))

series89.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ 1 (- (* (acos a) (/ 1 a))))
49.0ms	(* (acos a) (/ 1 a))

simplify4.4s

Counts

91 → 91

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	138	989
1	288	700
2	660	619
3	2163	581
done	5000	581

prune171.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes137.0ms

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

sample1.0s

Algorithm

intervals

Results

371.0ms	8000×	body	80	valid
206.0ms	7844×	body	80	nan