Details

sample1.1s

Algorithm

intervals

Results

460.0ms	262×	body	10240	exit
141.0ms	88×	body	2560	valid
61.0ms	87×	body	1280	valid
34.0ms	38×	body	640	valid
25.0ms	572×	body	80	nan
6.0ms	21×	body	320	valid
3.0ms	18×	body	160	valid
2.0ms	1×	body	5120	nan
1.0ms	1×	body	2560	nan
0.0ms	4×	body	80	valid
0.0ms	2×	body	160	nan

simplify46.0ms

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	5001	6
done	5001	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(log1p a)
2.4b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.0b	(fmod (cosh a) (* a a))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
1×	`acos-asin`

Counts

3 → 22

Calls

3 calls:

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

series16.0ms

Counts

3 → 9

Calls

3 calls:

1.0ms	(log1p a)
4.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
11.0ms	(fmod (cosh a) (* a a))

simplify85.0ms

Counts

31 → 31

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	52	167
1	81	144
2	167	144
3	419	144
4	1992	144
5	5001	144
done	5001	144

prune104.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 57.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p a)
2.4b	(acos (pow (fmod (cosh a) (* a a)) (log (exp (log1p a)))))
6.8b	(log (exp (log1p a)))
59.0b	(fmod (cosh a) (* a a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 37

Calls

4 calls:

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

series12.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(log1p a)
6.0ms	(acos (pow (fmod (cosh a) (* a a)) (log (exp (log1p a)))))
2.0ms	(log (exp (log1p a)))
3.0ms	(fmod (cosh a) (* a a))

simplify106.0ms

Counts

49 → 49

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	82	242
1	124	206
2	240	206
3	612	206
4	2966	206
5	5001	206
done	5001	206

prune159.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 57.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a)))))
1.2b	(- (/ PI 2) (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a))))))
6.8b	(log (exp (log1p a)))
59.0b	(fmod (cosh a) (* a a))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`add-cube-cbrt` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `log-pow` `add-cbrt-cube`
3×	`log-prod` `exp-prod`
2×	`asin-acos` `difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 46

Calls

4 calls:

1.0ms	(asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a)))))
20.0ms	(- (/ PI 2) (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a))))))
3.0ms	(log (exp (log1p a)))
0.0ms	(fmod (cosh a) (* a a))

series41.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a)))))
33.0ms	(- (/ PI 2) (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a))))))
2.0ms	(log (exp (log1p a)))
3.0ms	(fmod (cosh a) (* a a))

simplify139.0ms

Counts

58 → 58

Iterations

Useful iterations: 4 (134.0ms)

Iter	Nodes	Cost
0	153	493
1	306	438
2	716	436
3	2917	436
4	5002	434
done	5002	434

prune222.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 56.8b

localize22.0ms

Local error

Found 4 expressions with local error:

53.3b	(- (/ PI 2) (* (* (cbrt (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a)))))) (cbrt (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a))))))) (cbrt (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a))))))))
59.0b	(fmod (cosh a) (* a a))
59.0b	(fmod (cosh a) (* a a))
59.0b	(fmod (cosh a) (* a a))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 33

Calls

4 calls:

25.0ms	(- (/ PI 2) (* (* (cbrt (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a)))))) (cbrt (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a))))))) (cbrt (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a))))))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series40.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ PI 2) (* (* (cbrt (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a)))))) (cbrt (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a))))))) (cbrt (asin (pow (fmod (cosh a) (* a a)) (log (exp (log1p a))))))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))

simplify132.0ms

Counts

45 → 45

Iterations

Useful iterations: 4 (126.0ms)

Iter	Nodes	Cost
0	122	775
1	307	612
2	981	599
3	3765	557
4	5002	500
done	5002	500

prune190.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 56.7b

regimes268.0ms

Accuracy

0% (0.2b remaining)

Error of 57.8b against oracle of 57.6b and baseline of 57.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	98
1	21	98
done	21	98

end0.0ms

sample22.8s

Algorithm

intervals

Results

13.8s	7981×	body	10240	exit
5.1s	3227×	body	2560	valid
1.7s	2422×	body	1280	valid
689.0ms	16441×	body	80	nan
484.0ms	1251×	body	640	valid
178.0ms	667×	body	320	valid
65.0ms	320×	body	160	valid
21.0ms	10×	body	5120	nan
11.0ms	113×	body	80	valid
4.0ms	4×	body	2560	nan
4.0ms	7×	body	1280	nan
1.0ms	4×	body	640	nan
1.0ms	5×	body	320	nan
1.0ms	6×	body	160	nan