Details

sample1.4s

Algorithm

intervals

Results

845.0ms	270×	body	10240	exit
241.0ms	99×	body	2560	valid
97.0ms	78×	body	1280	valid
66.0ms	24×	body	320	valid
44.0ms	516×	body	80	nan
30.0ms	44×	body	640	valid
4.0ms	10×	body	160	valid
2.0ms	1×	body	2560	nan
1.0ms	1×	body	1280	nan
0.0ms	1×	body	80	valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	24	10
3	44	10
4	91	10
5	373	10
6	3269	10
done	5001	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.7b

localize12.0ms

Local error

Found 2 expressions with local error:

1.7b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
60.4b	(fmod (cosh a) (* a a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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`
1×	`acos-asin`

Counts

2 → 19

Calls

2 calls:

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

series26.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
19.0ms	(fmod (cosh a) (* a a))

simplify3.1s

Counts

25 → 25

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	33	277
1	55	277
2	102	245
3	172	245
4	303	245
5	810	245
6	3964	245
done	5000	245

prune131.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 60.3b

localize18.0ms

Local error

Found 3 expressions with local error:

1.7b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
10.4b	(log (exp (fmod (cosh a) (* a a))))
60.4b	(fmod (cosh a) (* a a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 36

Calls

3 calls:

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

series13.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
4.0ms	(log (exp (fmod (cosh a) (* a a))))
3.0ms	(fmod (cosh a) (* a a))

simplify3.5s

Counts

45 → 45

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	57	521
1	89	460
2	154	409
3	236	409
4	382	409
5	971	409
6	4705	409
done	5001	409

prune257.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 60.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))))
0.8b	(expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a))))
1.7b	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
60.4b	(fmod (cosh a) (pow a 2))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

0.0ms	(log1p (expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))))
0.0ms	(expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a))))
1.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
0.0ms	(fmod (cosh a) (pow a 2))

series306.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(log1p (expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))))
95.0ms	(expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a))))
4.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
3.0ms	(fmod (cosh a) (pow a 2))

simplify715.0ms

Counts

53 → 53

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	50	670
1	78	638
2	149	564
3	469	562
done	5001	562

prune292.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 60.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a))))
1.0b	(log (exp (expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a))))))
1.7b	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
60.4b	(fmod (cosh a) (pow a 2))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

0.0ms	(expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a))))
3.0ms	(log (exp (expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a))))))
1.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
0.0ms	(fmod (cosh a) (pow a 2))

series141.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a))))
62.0ms	(log (exp (expm1 (acos (pow (fmod (cosh a) (pow a 2)) (log1p a))))))
5.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
3.0ms	(fmod (cosh a) (pow a 2))

simplify3.9s

Counts

60 → 60

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	65	836
1	100	781
2	204	693
3	529	693
4	2645	693
done	5000	693

prune290.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 60.3b

regimes40.0ms

Accuracy

0% (0.4b remaining)

Error of 60.2b against oracle of 59.9b and baseline of 60.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
done	9	12

end0.0ms

sample34.3s

Algorithm

intervals

Results

19.9s	8061×	body	10240	exit
7.1s	3142×	body	2560	valid
2.6s	2499×	body	1280	valid
1.8s	16376×	body	80	nan
1.3s	1295×	body	640	valid
327.0ms	637×	body	320	valid
91.0ms	314×	body	160	valid
21.0ms	113×	body	80	valid
18.0ms	6×	body	5120	nan
15.0ms	11×	body	2560	nan
5.0ms	12×	body	640	nan
3.0ms	3×	body	1280	nan
2.0ms	5×	body	320	nan
2.0ms	8×	body	160	nan