Details

sample695.0ms

Algorithm

intervals

Results

500.0ms	240×	body	10240	exit
57.0ms	69×	body	1280	valid
37.0ms	91×	body	80	valid
22.0ms	55×	body	640	valid
16.0ms	7×	body	2560	valid
7.0ms	132×	body	80	nan
7.0ms	24×	body	320	valid
2.0ms	1×	body	5120	valid
1.0ms	9×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(cosh c)
38.2b	(fmod (cosh c) (log1p a))

rewrite33.0ms

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:

31.0ms	(cosh c)
1.0ms	(fmod (cosh c) (log1p a))

series80.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(cosh c)
18.0ms	(fmod (cosh c) (log1p a))

simplify2.4s

Counts

25 → 25

Iterations

Iter	Nodes
done	5001
4	3280
3	675
2	199
1	79
0	44

prune229.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 33.4b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* 1/2 c) c (fma (pow c 4) 1/24 1))
0.0b	(fma (pow c 4) 1/24 1)
38.0b	(fmod (fma (* 1/2 c) c (fma (pow c 4) 1/24 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:

1.0ms	(fma (* 1/2 c) c (fma (pow c 4) 1/24 1))
1.0ms	(fma (pow c 4) 1/24 1)
0.0ms	(fmod (fma (* 1/2 c) c (fma (pow c 4) 1/24 1)) (log1p a))

series196.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(fma (* 1/2 c) c (fma (pow c 4) 1/24 1))
124.0ms	(fma (pow c 4) 1/24 1)
9.0ms	(fmod (fma (* 1/2 c) c (fma (pow c 4) 1/24 1)) (log1p a))

simplify2.7s

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
3	2444
2	299
1	74
0	47

prune309.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 33.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (* (pow c 4) 1/24))
0.0b	(exp (log1p (* (pow c 4) 1/24)))
0.1b	(* (pow c 4) 1/24)
38.0b	(fmod (fma (* 1/2 c) c (exp (log1p (* (pow c 4) 1/24)))) (log1p a))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`add-exp-log`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
6×	`add-cbrt-cube`
5×	`expm1-log1p-u` `add-log-exp`
4×	`pow1` `unpow-prod-down` `log1p-expm1-u`
3×	`exp-prod` `associate-r` `prod-exp` `unswap-sqr`
2×	`log1p-udef` `sqr-pow` `rem-exp-log`
1×	`pow-to-exp` `pow-exp` `log1p-expm1` `*-commutative` `cbrt-unprod`

Counts

4 → 61

Calls

4 calls:

0.0ms	(log1p (* (pow c 4) 1/24))
2.0ms	(exp (log1p (* (pow c 4) 1/24)))
14.0ms	(* (pow c 4) 1/24)
0.0ms	(fmod (fma (* 1/2 c) c (exp (log1p (* (pow c 4) 1/24)))) (log1p a))

series4.2s

Counts

4 → 12

Calls

4 calls:

2.2s	(log1p (* (pow c 4) 1/24))
2.0s	(exp (log1p (* (pow c 4) 1/24)))
73.0ms	(* (pow c 4) 1/24)
6.0ms	(fmod (fma (* 1/2 c) c (exp (log1p (* (pow c 4) 1/24)))) (log1p a))

simplify655.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	888
1	268
0	130

prune519.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (log1p (* 1/24 (pow c 4)))) (sqrt (log1p (* 1/24 (pow c 4)))))
17.0b	(sqrt (log1p (* 1/24 (pow c 4))))
17.0b	(sqrt (log1p (* 1/24 (pow c 4))))
38.0b	(fmod (fma (* 1/2 c) c (exp (* (sqrt (log1p (* 1/24 (pow c 4)))) (sqrt (log1p (* 1/24 (pow c 4))))))) (log1p a))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

11.0ms	(* (sqrt (log1p (* 1/24 (pow c 4)))) (sqrt (log1p (* 1/24 (pow c 4)))))
1.0ms	(sqrt (log1p (* 1/24 (pow c 4))))
1.0ms	(sqrt (log1p (* 1/24 (pow c 4))))
0.0ms	(fmod (fma (* 1/2 c) c (exp (* (sqrt (log1p (* 1/24 (pow c 4)))) (sqrt (log1p (* 1/24 (pow c 4))))))) (log1p a))

series6.0s

Counts

4 → 12

Calls

4 calls:

1.9s	(* (sqrt (log1p (* 1/24 (pow c 4)))) (sqrt (log1p (* 1/24 (pow c 4)))))
2.1s	(sqrt (log1p (* 1/24 (pow c 4))))
1.9s	(sqrt (log1p (* 1/24 (pow c 4))))
10.0ms	(fmod (fma (* 1/2 c) c (exp (* (sqrt (log1p (* 1/24 (pow c 4)))) (sqrt (log1p (* 1/24 (pow c 4))))))) (log1p a))

simplify813.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1311
1	375
0	160

prune694.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 33.2b

regimes752.0ms

Accuracy

0% (0.4b remaining)

Error of 34.8b against oracle of 34.4b and baseline of 34.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	15

end0.0ms

sample16.6s

Algorithm

intervals

Results

11.6s	7997×	body	10240	exit
2.2s	2370×	body	1280	valid
745.0ms	5395×	body	80	nan
525.0ms	1585×	body	640	valid
288.0ms	2685×	body	80	valid
241.0ms	162×	body	2560	valid
159.0ms	786×	body	320	valid
59.0ms	403×	body	160	valid
18.0ms	9×	body	5120	valid