Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
5.0ms	288×	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: 0.3b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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:

7.0ms

(/ a (- (acos a)))

series31.0ms

Counts

1 → 3

Calls

1 calls:

31.0ms

(/ a (- (acos a)))

simplify4.9s

Counts

60 → 60

Iterations

Useful iterations: 5 (1.9s)

Iter	Nodes	Cost
0	96	613
1	166	581
2	333	563
3	587	563
4	1105	563
5	2150	558
done	5001	558

prune183.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite40.0ms

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:

17.0ms	(/ 1 (- (/ (acos a) a)))
6.0ms	(/ (acos a) a)

series77.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ 1 (- (/ (acos a) a)))
41.0ms	(/ (acos a) a)

simplify6.5s

Counts

178 → 178

Iterations

Useful iterations: 3 (1.2s)

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

prune347.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

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))
0.6b	(* (cbrt (/ (acos a) a)) (cbrt (/ (acos a) a)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 152

Calls

4 calls:

2.0ms	(cbrt (/ (acos a) a))
2.0ms	(cbrt (/ (acos a) a))
2.0ms	(cbrt (/ (acos a) a))
57.0ms	(* (cbrt (/ (acos a) a)) (cbrt (/ (acos a) a)))

series1.0s

Counts

4 → 12

Calls

4 calls:

267.0ms	(cbrt (/ (acos a) a))
190.0ms	(cbrt (/ (acos a) a))
280.0ms	(cbrt (/ (acos a) a))
279.0ms	(* (cbrt (/ (acos a) a)) (cbrt (/ (acos a) a)))

simplify3.1s

Counts

164 → 164

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	164	2249
1	277	2118
2	690	2038
3	1314	1930
4	3218	1798
done	5000	1664

prune625.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ (cbrt (acos a)) a)) (cbrt (/ (cbrt (acos a)) a)))
1.0b	(cbrt (acos a))
1.0b	(cbrt (acos a))
1.0b	(* (cbrt (pow (acos a) 2/3)) (cbrt (pow (acos a) 2/3)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

214×	`cbrt-prod`
146×	`add-sqr-sqrt`
88×	`times-frac`
74×	`add-cube-cbrt` `*-un-lft-identity`
35×	`swap-sqr` `associate-r` `associate-l`
32×	`unswap-sqr`
20×	`unpow-prod-down`
18×	`pow1`
14×	`pow1/3`
12×	`sqr-pow`
8×	`add-exp-log`
4×	`expm1-log1p-u` `cbrt-div` `pow-prod-down` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`frac-times` `associate-r/` `associate-l/`

Counts

4 → 206

Calls

4 calls:

49.0ms	(* (cbrt (/ (cbrt (acos a)) a)) (cbrt (/ (cbrt (acos a)) a)))
1.0ms	(cbrt (acos a))
1.0ms	(cbrt (acos a))
24.0ms	(* (cbrt (pow (acos a) 2/3)) (cbrt (pow (acos a) 2/3)))

series1.2s

Counts

4 → 12

Calls

4 calls:

536.0ms	(* (cbrt (/ (cbrt (acos a)) a)) (cbrt (/ (cbrt (acos a)) a)))
183.0ms	(cbrt (acos a))
194.0ms	(cbrt (acos a))
257.0ms	(* (cbrt (pow (acos a) 2/3)) (cbrt (pow (acos a) 2/3)))

simplify2.9s

Counts

218 → 218

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	272	3746
1	413	3383
2	1065	3102
3	2406	2971
done	5000	2960

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes117.0ms

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

sample922.0ms

Algorithm

intervals

Results

398.0ms	8000×	body	80	valid
176.0ms	8037×	body	80	nan