Details

sample125.0ms

Algorithm

intervals

Results

30.0ms	46×	body	10240	exit
27.0ms	43×	body	1280	valid
19.0ms	51×	body	640	valid
9.0ms	122×	body	80	valid
5.0ms	27×	body	320	valid
5.0ms	2×	body	2560	valid
4.0ms	83×	body	80	nan
2.0ms	12×	body	160	valid
2.0ms	6×	body	1280	nan
1.0ms	5×	body	640	nan
1.0ms	4×	body	320	nan
0.0ms	2×	body	160	nan

simplify826.0ms

Counts

1 → 1

Iterations

Useful iterations: 11 (409.0ms)

Iter	Nodes	Cost
0	12	13
1	20	13
2	35	12
3	51	12
4	77	12
5	105	12
6	137	12
7	176	12
8	217	12
9	278	12
10	456	12
11	508	10
12	535	10
done	535	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (log (fma y (expm1 z) 1.0)) t)
3.3b	(log (fma y (expm1 z) 1.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`pow1`
5×	`add-exp-log` `log-pow`
4×	`add-cbrt-cube` `associate-/l*`
3×	`log-prod` `associate-/r*`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

2 → 47

Calls

2 calls:

3.0ms	(/ (log (fma y (expm1 z) 1.0)) t)
1.0ms	(log (fma y (expm1 z) 1.0))

series231.0ms

Counts

2 → 6

Calls

2 calls:

155.0ms	(/ (log (fma y (expm1 z) 1.0)) t)
76.0ms	(log (fma y (expm1 z) 1.0))

simplify1.1s

Counts

53 → 53

Iterations

Useful iterations: 3 (547.0ms)

Iter	Nodes	Cost
0	140	784
1	303	749
2	891	684
3	2951	680
done	5001	680

prune179.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fma y (expm1 z) 1.0))
0.1b	(cbrt (fma y (expm1 z) 1.0))
3.4b	(log (cbrt (fma y (expm1 z) 1.0)))
3.4b	(log (cbrt (fma y (expm1 z) 1.0)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow1/3` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-log-exp`

Counts

4 → 62

Calls

4 calls:

0.0ms	(cbrt (fma y (expm1 z) 1.0))
0.0ms	(cbrt (fma y (expm1 z) 1.0))
1.0ms	(log (cbrt (fma y (expm1 z) 1.0)))
1.0ms	(log (cbrt (fma y (expm1 z) 1.0)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (fma y (expm1 z) 1.0))
155.0ms	(cbrt (fma y (expm1 z) 1.0))
141.0ms	(log (cbrt (fma y (expm1 z) 1.0)))
142.0ms	(log (cbrt (fma y (expm1 z) 1.0)))

simplify884.0ms

Counts

74 → 74

Iterations

Useful iterations: done (881.0ms)

Iter	Nodes	Cost
0	110	1166
1	262	1088
2	751	994
3	2712	946
done	5000	944

prune331.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (sqrt (fma y (expm1 z) 1.0)))
3.4b	(log (cbrt (fma y (expm1 z) 1.0)))
3.4b	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))
3.4b	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
21×	`cbrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
7×	`pow1` `add-exp-log`
6×	`log-pow`
4×	`expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`

Counts

4 → 76

Calls

4 calls:

1.0ms	(cbrt (sqrt (fma y (expm1 z) 1.0)))
1.0ms	(log (cbrt (fma y (expm1 z) 1.0)))
1.0ms	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))
2.0ms	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))

series620.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (sqrt (fma y (expm1 z) 1.0)))
144.0ms	(log (cbrt (fma y (expm1 z) 1.0)))
187.0ms	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))
193.0ms	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))

simplify1.1s

Counts

88 → 88

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	164	1420
1	369	1319
2	1017	1206
3	3404	1173
done	5001	1171

prune446.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (sqrt (fma y (expm1 z) 1.0)))
3.3b	(log (fma y (expm1 z) 1.0))
3.4b	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))
3.4b	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

21×	`log-prod`
18×	`cbrt-prod`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
7×	`pow1` `add-exp-log`
5×	`log-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

1.0ms	(cbrt (sqrt (fma y (expm1 z) 1.0)))
1.0ms	(log (fma y (expm1 z) 1.0))
1.0ms	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))
1.0ms	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (sqrt (fma y (expm1 z) 1.0)))
81.0ms	(log (fma y (expm1 z) 1.0))
198.0ms	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))
196.0ms	(log (cbrt (sqrt (fma y (expm1 z) 1.0))))

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	152	1336
1	345	1240
2	983	1130
3	3405	1101
done	5000	1099

prune407.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.3b

regimes181.0ms

Accuracy

43.3% (3.9b remaining)

Error of 8.5b against oracle of 4.6b and baseline of 11.5b

bsearch82.0ms

Steps

Iters	Range		Point
8	-4.8152653812927384e-08	-8.345203094607524e-13	-3.93535345747879e-11

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	62
1	41	62
done	41	62

end0.0ms

sample3.1s

Algorithm

intervals

Results

747.0ms	1490×	body	10240	exit
746.0ms	1406×	body	1280	valid
475.0ms	1612×	body	640	valid
211.0ms	3515×	body	80	valid
165.0ms	903×	body	320	valid
109.0ms	84×	body	2560	valid
91.0ms	2485×	body	80	nan
56.0ms	502×	body	160	valid
52.0ms	264×	body	640	nan
30.0ms	104×	body	1280	nan
26.0ms	197×	body	320	nan
9.0ms	115×	body	160	nan