Details

sample1.0s

Algorithm

intervals

Results

426.0ms	248×	body	10240	exit
158.0ms	98×	body	2560	valid
58.0ms	81×	body	1280	valid
38.0ms	436×	body	80	nan
17.0ms	44×	body	640	valid
4.0ms	15×	body	320	valid
3.0ms	15×	body	160	valid
0.0ms	1×	body	640	nan
0.0ms	3×	body	80	valid

simplify45.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	6
1	24	6
2	43	6
3	91	6
4	257	6
5	1277	6
6	5002	6
done	5002	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (fmod (cosh a) (* a a)) (log1p a))
2.0b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
58.5b	(fmod (cosh a) (* a a))

rewrite13.0ms

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))

series64.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(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))

simplify103.0ms

Counts

47 → 47

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	220	450
1	820	423
2	3551	413
3	5001	405
done	5001	405

prune169.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 59.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fmod (cosh a) (* a a)))
2.0b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
12.7b	(log (exp (fmod (cosh a) (* a a))))
58.5b	(fmod (cosh a) (* a a))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

2.0ms	(exp (fmod (cosh a) (* a a)))
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))

series39.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(exp (fmod (cosh a) (* a a)))
4.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(fmod (cosh a) (* a a))

simplify126.0ms

Counts

61 → 61

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	88	383
1	133	336
2	257	336
3	681	336
4	3339	336
5	5002	336
done	5002	336

prune222.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 59.3b

localize17.0ms

Local error

Found 4 expressions with local error:

12.7b	(log (exp (fmod (cosh a) (* a a))))
58.5b	(fmod (cosh a) (* a a))
58.5b	(fmod (cosh a) (* a a))
58.5b	(fmod (cosh a) (* a a))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

3.0ms	(log (exp (fmod (cosh a) (* a a))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series10.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))

simplify82.0ms

Counts

56 → 56

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	56	278
1	79	244
2	161	244
3	412	244
4	1977	244
5	5001	244
done	5001	244

prune285.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 59.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.1b	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
12.7b	(log (exp (fmod (cosh a) (* a a))))
58.5b	(fmod (cosh a) (* a a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
39×	`prod-diff`
37×	`times-frac`
13×	`fma-neg`
6×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`log-prod` `exp-prod`
2×	`asin-acos` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 106

Calls

4 calls:

1.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
22.0ms	(- (/ PI 2) (asin (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))

series39.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
31.0ms	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(fmod (cosh a) (* a a))

simplify179.0ms

Counts

118 → 118

Iterations

Useful iterations: 3 (160.0ms)

Iter	Nodes	Cost
0	309	2819
1	761	1452
2	4112	1425
3	5001	1396
done	5001	1396

prune320.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 59.3b

regimes207.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	22
1	36	22
2	44	22
3	44	22
done	44	22

end0.0ms

sample22.3s

Algorithm

intervals

Results

13.4s	7785×	body	10240	exit
5.0s	3180×	body	2560	valid
1.8s	2510×	body	1280	valid
660.0ms	15577×	body	80	nan
477.0ms	1252×	body	640	valid
168.0ms	628×	body	320	valid
58.0ms	309×	body	160	valid
25.0ms	12×	body	5120	nan
12.0ms	121×	body	80	valid
4.0ms	7×	body	1280	nan
3.0ms	3×	body	2560	nan
2.0ms	9×	body	320	nan
1.0ms	4×	body	640	nan
1.0ms	5×	body	160	nan