Details

sample889.0ms

Algorithm

intervals

Results

424.0ms	89×	body	1280	valid
374.0ms	235×	body	10240	exit
22.0ms	54×	body	640	valid
13.0ms	9×	body	2560	valid
10.0ms	178×	body	80	nan
6.0ms	77×	body	80	valid
5.0ms	19×	body	320	valid
2.0ms	1×	body	5120	valid
1.0ms	7×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
3	16
2	14
1	11
0	5

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize48.0ms

Local error

Found 2 expressions with local error:

0.0b	(cosh c)
41.7b	(fmod (cosh c) (log1p a))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
1×	`cosh-def`

Counts

2 → 15

Calls

2 calls:

3.0ms	(cosh c)
1.0ms	(fmod (cosh c) (log1p a))

series102.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(cosh c)
17.0ms	(fmod (cosh c) (log1p a))

simplify4.4s

Counts

21 → 21

Iterations

Iter	Nodes
done	5011
5	4210
4	902
3	292
2	130
1	73
0	40

prune152.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 36.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (* c c) (+ 1/2 (* 1/24 (* c c))))
0.2b	(* 1/24 (* c c))
41.5b	(fmod (+ 1 (* (* c c) (+ 1/2 (* 1/24 (* c c))))) (log1p a))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `associate-l`
3×	`add-log-exp`
2×	`associate-r/` `-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

3 → 49

Calls

3 calls:

24.0ms	(* (* c c) (+ 1/2 (* 1/24 (* c c))))
29.0ms	(* 1/24 (* c c))
0.0ms	(fmod (+ 1 (* (* c c) (+ 1/2 (* 1/24 (* c c))))) (log1p a))

series172.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(* (* c c) (+ 1/2 (* 1/24 (* c c))))
32.0ms	(* 1/24 (* c c))
8.0ms	(fmod (+ 1 (* (* c c) (+ 1/2 (* 1/24 (* c c))))) (log1p a))

simplify1.4s

Counts

58 → 58

Iterations

Iter	Nodes
done	5007
2	1119
1	273
0	91

prune311.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 36.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* c c) 1/2)
0.1b	(* (* c c) (* 1/24 (* c c)))
0.2b	(* 1/24 (* c c))
41.5b	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

35×	`pow1` `add-cbrt-cube` `add-exp-log`
21×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`

Counts

4 → 73

Calls

4 calls:

14.0ms	(* (* c c) 1/2)
60.0ms	(* (* c c) (* 1/24 (* c c)))
13.0ms	(* 1/24 (* c c))
0.0ms	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))

series155.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* c c) 1/2)
49.0ms	(* (* c c) (* 1/24 (* c c)))
49.0ms	(* 1/24 (* c c))
14.0ms	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))

simplify3.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	3356
2	889
1	261
0	100

prune518.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 36.5b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/24 (* c c))
41.5b	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))
41.5b	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))
41.5b	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 40

Calls

4 calls:

35.0ms	(* 1/24 (* c c))
0.0ms	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))
0.0ms	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))
0.0ms	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))

series90.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* 1/24 (* c c))
12.0ms	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))
13.0ms	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))
15.0ms	(fmod (+ 1 (+ (* (* c c) 1/2) (* (* c c) (* 1/24 (* c c))))) (log1p a))

simplify2.0s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	1556
2	387
1	131
0	57

prune414.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 36.5b

regimes629.0ms

Accuracy

0% (0.2b remaining)

Error of 34.9b against oracle of 34.7b and baseline of 34.9b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	19

end0.0ms

sample19.4s

Algorithm

intervals

Results

13.7s	7934×	body	10240	exit
1.8s	2363×	body	1280	valid
1.0s	1591×	body	640	valid
822.0ms	5390×	body	80	nan
499.0ms	429×	body	160	valid
251.0ms	2688×	body	80	valid
237.0ms	136×	body	2560	valid
221.0ms	778×	body	320	valid
76.0ms	15×	body	5120	valid