Details

sample1.2s

Algorithm

intervals

Results

744.0ms	267×	body	10240	exit
193.0ms	92×	body	2560	valid
85.0ms	83×	body	1280	valid
42.0ms	550×	body	80	nan
26.0ms	47×	body	640	valid
8.0ms	19×	body	320	valid
4.0ms	1×	body	5120	nan
4.0ms	13×	body	160	valid
3.0ms	2×	body	1280	nan
0.0ms	2×	body	80	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	24	10
3	44	10
4	89	10
5	195	10
6	633	10
7	2582	10
done	5000	10

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (fmod (cosh a) (* a a)) (log1p a))
2.6b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.5b	(fmod (cosh a) (* a a))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `unpow-prod-down` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

3 → 38

Calls

3 calls:

4.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
1.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series77.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
4.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
10.0ms	(fmod (cosh a) (* a a))

simplify2.0s

Counts

47 → 47

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	99	779
1	218	752
2	595	710
3	2177	659
done	5000	656

prune300.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 59.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
2.6b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
13.4b	(log (exp (fmod (cosh a) (* a a))))
59.5b	(fmod (cosh a) (* a a))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`log-pow`
7×	`pow1` `unpow-prod-down`
6×	`exp-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-prod`
1×	`acos-asin` `pow-to-exp` `pow-pow` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

10.0ms	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
2.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
5.0ms	(log (exp (fmod (cosh a) (* a a))))
1.0ms	(fmod (cosh a) (* a a))

series87.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
4.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
4.0ms	(log (exp (fmod (cosh a) (* a a))))
5.0ms	(fmod (cosh a) (* a a))

simplify2.1s

Counts

71 → 71

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	128	1155
1	250	1003
2	631	942
3	2239	891
done	5000	888

prune370.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 59.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (fmod (cosh a) (* a a)) (log1p a))
1.3b	(log (exp (acos (pow (fmod (cosh a) (* a a)) (log1p a)))))
2.6b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.5b	(fmod (cosh a) (* a a))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `log-prod` `exp-prod`
2×	`acos-asin`
1×	`pow-to-exp` `log-div` `pow-pow` `exp-diff` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

4 → 56

Calls

4 calls:

3.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
9.0ms	(log (exp (acos (pow (fmod (cosh a) (* a a)) (log1p a)))))
1.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
0.0ms	(fmod (cosh a) (* a a))

series78.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
4.0ms	(log (exp (acos (pow (fmod (cosh a) (* a a)) (log1p a)))))
4.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
3.0ms	(fmod (cosh a) (* a a))

simplify2.2s

Counts

68 → 68

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	126	1114
1	250	1048
2	632	975
3	2234	924
done	5000	921

prune404.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 59.8b

localize25.0ms

Local error

Found 4 expressions with local error:

2.6b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
2.6b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.5b	(fmod (cosh a) (* a a))
59.5b	(fmod (cosh a) (* a a))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`acos-asin`

Counts

4 → 38

Calls

4 calls:

2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
0.0ms	(fmod (cosh a) (* a a))
1.0ms	(fmod (cosh a) (* a a))

series24.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
7.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
5.0ms	(fmod (cosh a) (* a a))
5.0ms	(fmod (cosh a) (* a a))

simplify3.6s

Counts

50 → 50

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	33	554
1	47	554
2	65	490
3	94	490
4	152	490
5	294	490
6	776	490
7	2892	490
done	5000	490

prune365.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 59.8b

regimes453.0ms

Accuracy

0% (0.4b remaining)

Error of 60.2b against oracle of 59.8b and baseline of 60.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	31
1	22	31
done	22	31

end0.0ms

sample38.8s

Algorithm

intervals

Results

23.3s	7831×	body	10240	exit
8.1s	3111×	body	2560	valid
3.2s	2543×	body	1280	valid
1.8s	15913×	body	80	nan
835.0ms	1272×	body	640	valid
283.0ms	644×	body	320	valid
100.0ms	310×	body	160	valid
30.0ms	9×	body	5120	nan
20.0ms	120×	body	80	valid
7.0ms	9×	body	1280	nan
4.0ms	7×	body	640	nan
3.0ms	6×	body	320	nan
2.0ms	10×	body	160	nan
2.0ms	1×	body	2560	nan