Details

sample1.1s

Algorithm

intervals

Results

672.0ms	81×	body	10240	exit
199.0ms	81×	body	1280	valid
52.0ms	46×	body	640	valid
15.0ms	93×	body	80	valid
13.0ms	24×	body	320	valid
7.0ms	12×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 21

Calls

3 calls:

0.0ms	(expm1 (sin (expm1 a)))
4.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series137.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(expm1 (sin (expm1 a)))
113.0ms	(sin (expm1 a))
21.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.0s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
8	3071
7	934
6	395
5	166
4	66
3	44
2	35
1	31
0	28

prune236.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 32.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (expm1 a)))
0.5b	(cbrt (sin (expm1 a)))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
37.9b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
1.0ms	(cbrt (sin (expm1 a)))
13.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series737.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(cbrt (sin (expm1 a)))
219.0ms	(cbrt (sin (expm1 a)))
283.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify1.9s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	499
1	120
0	63

prune661.0ms

Pruning

27 alts after pruning (25 fresh and 2 done)

Merged error: 31.4b

localize92.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (expm1 a)))
0.5b	(cbrt (sin (expm1 a)))
0.5b	(cbrt (sin (expm1 a)))
37.9b	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cbrt (sin (expm1 a)))
2.0ms	(cbrt (sin (expm1 a)))
2.0ms	(cbrt (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series726.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(cbrt (sin (expm1 a)))
218.0ms	(cbrt (sin (expm1 a)))
308.0ms	(cbrt (sin (expm1 a)))
9.0ms	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify1.3s

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
3	665
2	160
1	58
0	35

prune619.0ms

Pruning

34 alts after pruning (32 fresh and 2 done)

Merged error: 31.3b

localize133.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (expm1 a)))
0.5b	(cbrt (sin (expm1 a)))
0.6b	(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
37.9b	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
18×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`pow1/3`
9×	`-un-lft-identity` `associate-r*` `add-exp-log` `pow-prod-up` `add-cube-cbrt`
6×	`pow-plus`
5×	`add-cbrt-cube` `pow-prod-down`
4×	`add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod` `unswap-sqr`
2×	`pow2`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 68

Calls

4 calls:

2.0ms	(cbrt (sin (expm1 a)))
2.0ms	(cbrt (sin (expm1 a)))
66.0ms	(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
0.0ms	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

series858.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(cbrt (sin (expm1 a)))
318.0ms	(cbrt (sin (expm1 a)))
280.0ms	(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
10.0ms	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

simplify1.3s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	811
1	170
0	79

prune446.0ms

Pruning

35 alts after pruning (33 fresh and 2 done)

Merged error: 31.2b

regimes1.1s

Accuracy

0% (1.9b remaining)

Error of 33.8b against oracle of 32.0b and baseline of 33.8b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample22.6s

Algorithm

intervals

Results

10.8s	2585×	body	10240	exit
6.8s	2281×	body	1280	valid
2.0s	1720×	body	640	valid
1.3s	821×	body	320	valid
985.0ms	2763×	body	80	valid
243.0ms	408×	body	160	valid
27.0ms	4×	body	5120	valid
10.0ms	3×	body	2560	valid