Details

sample935.0ms

Algorithm

intervals

Results

455.0ms	19×	body	320	valid
338.0ms	235×	body	10240	exit
63.0ms	89×	body	1280	valid
19.0ms	54×	body	640	valid
12.0ms	9×	body	2560	valid
8.0ms	178×	body	80	nan
5.0ms	77×	body	80	valid
1.0ms	7×	body	160	valid
1.0ms	1×	body	5120	valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize54.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
1×	`cosh-def`

Counts

2 → 19

Calls

2 calls:

3.0ms	(cosh c)
4.0ms	(fmod (cosh c) (log1p a))

series104.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(cosh c)
17.0ms	(fmod (cosh c) (log1p a))

simplify2.1s

Counts

25 → 25

Iterations

Iter	Nodes
done	5000
5	1864
4	743
3	314
2	144
1	79
0	44

prune196.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 36.6b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`

Counts

3 → 29

Calls

3 calls:

0.0ms	(fma (* c c) (fma 1/24 (* c c) 1/2) 1)
1.0ms	(fma 1/24 (* c c) 1/2)
0.0ms	(fmod (fma (* c c) (fma 1/24 (* c c) 1/2) 1) (log1p a))

series178.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(fma (* c c) (fma 1/24 (* c c) 1/2) 1)
104.0ms	(fma 1/24 (* c c) 1/2)
10.0ms	(fmod (fma (* c c) (fma 1/24 (* c c) 1/2) 1) (log1p a))

simplify1.2s

Counts

38 → 38

Iterations

Iter	Nodes
done	5014
3	954
2	208
1	91
0	52

prune257.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 36.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/24 (* c c) 1/2)
0.0b	(log (fma 1/24 (* c c) 1/2))
0.0b	(exp (log (fma 1/24 (* c c) 1/2)))
41.5b	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

0.0ms	(fma 1/24 (* c c) 1/2)
1.0ms	(log (fma 1/24 (* c c) 1/2))
3.0ms	(exp (log (fma 1/24 (* c c) 1/2)))
0.0ms	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))

series262.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(fma 1/24 (* c c) 1/2)
85.0ms	(log (fma 1/24 (* c c) 1/2))
66.0ms	(exp (log (fma 1/24 (* c c) 1/2)))
11.0ms	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))

simplify3.0s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
4	4022
3	1053
2	365
1	170
0	93

prune474.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 36.5b

localize106.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))) (cbrt (fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))))
41.5b	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))
41.5b	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))
41.5b	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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:

9.0ms	(* (cbrt (fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))) (cbrt (fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))))
0.0ms	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))
0.0ms	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))
0.0ms	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))

series147.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (cbrt (fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))) (cbrt (fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))))
10.0ms	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))
7.0ms	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))
6.0ms	(fmod (fma (* c c) (exp (log (fma 1/24 (* c c) 1/2))) 1) (log1p a))

simplify2.7s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
4	1746
3	618
2	289
1	132
0	65

prune657.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 36.5b

regimes1.0s

Accuracy

0% (0.2b remaining)

Error of 34.8b against oracle of 34.7b and baseline of 34.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	16

end0.0ms

sample19.0s

Algorithm

intervals

Results

13.5s	7934×	body	10240	exit
1.9s	2363×	body	1280	valid
1.2s	1591×	body	640	valid
878.0ms	5390×	body	80	nan
285.0ms	136×	body	2560	valid
207.0ms	778×	body	320	valid
192.0ms	2688×	body	80	valid
185.0ms	429×	body	160	valid
37.0ms	15×	body	5120	valid