Details

sample102.0ms

Algorithm

intervals

Results

24.0ms	43×	body	1280	valid
23.0ms	46×	body	10240	exit
15.0ms	51×	body	640	valid
7.0ms	122×	body	80	valid
5.0ms	27×	body	320	valid
4.0ms	2×	body	2560	valid
3.0ms	83×	body	80	nan
2.0ms	6×	body	1280	nan
1.0ms	12×	body	160	valid
1.0ms	5×	body	640	nan
1.0ms	4×	body	320	nan
0.0ms	2×	body	160	nan

simplify19.1s

Counts

1 → 1

Iterations

Useful iterations: 8 (167.0ms)

Iter	Nodes	Cost
0	12	13
1	20	13
2	35	12
3	51	12
4	78	12
5	134	12
6	204	12
7	288	12
8	477	10
9	719	10
10	885	10
11	934	10
12	1264	10
13	3672	10
done	5000	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 (expm1 z) y 1.0)) t)
3.3b	(log (fma (expm1 z) y 1.0))

rewrite8.0ms

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

series182.0ms

Counts

2 → 6

Calls

2 calls:

122.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
59.0ms	(log (fma (expm1 z) y 1.0))

simplify2.5s

Counts

53 → 53

Iterations

Useful iterations: 3 (360.0ms)

Iter	Nodes	Cost
0	130	750
1	279	718
2	956	656
3	4588	652
done	5000	652

prune181.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fma (expm1 z) y 1.0))
0.1b	(cbrt (fma (expm1 z) y 1.0))
3.4b	(log (cbrt (fma (expm1 z) y 1.0)))
3.4b	(log (cbrt (fma (expm1 z) y 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 (expm1 z) y 1.0))
0.0ms	(cbrt (fma (expm1 z) y 1.0))
1.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
1.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (fma (expm1 z) y 1.0))
110.0ms	(cbrt (fma (expm1 z) y 1.0))
117.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
121.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify1.4s

Counts

74 → 74

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	110	1166
1	262	1090
2	818	994
3	3787	946
done	5000	944

prune331.0ms

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 (expm1 z) y 1.0)))
3.4b	(log (cbrt (fma (expm1 z) y 1.0)))
3.4b	(log (cbrt (sqrt (fma (expm1 z) y 1.0))))
3.4b	(log (cbrt (sqrt (fma (expm1 z) y 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 (expm1 z) y 1.0)))
1.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
1.0ms	(log (cbrt (sqrt (fma (expm1 z) y 1.0))))
2.0ms	(log (cbrt (sqrt (fma (expm1 z) y 1.0))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (sqrt (fma (expm1 z) y 1.0)))
123.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
118.0ms	(log (cbrt (sqrt (fma (expm1 z) y 1.0))))
122.0ms	(log (cbrt (sqrt (fma (expm1 z) y 1.0))))

simplify1.8s

Counts

88 → 88

Iterations

Useful iterations: 3 (414.0ms)

Iter	Nodes	Cost
0	163	1422
1	368	1329
2	1117	1206
3	4887	1173
done	5000	1173

prune432.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (sqrt (fma (expm1 z) y 1.0)))
3.3b	(log (fma (expm1 z) y 1.0))
3.4b	(log (cbrt (sqrt (fma (expm1 z) y 1.0))))
3.4b	(log (cbrt (sqrt (fma (expm1 z) y 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 (expm1 z) y 1.0)))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (cbrt (sqrt (fma (expm1 z) y 1.0))))
2.0ms	(log (cbrt (sqrt (fma (expm1 z) y 1.0))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt (sqrt (fma (expm1 z) y 1.0)))
59.0ms	(log (fma (expm1 z) y 1.0))
122.0ms	(log (cbrt (sqrt (fma (expm1 z) y 1.0))))
119.0ms	(log (cbrt (sqrt (fma (expm1 z) y 1.0))))

simplify1.7s

Counts

84 → 84

Iterations

Useful iterations: 3 (366.0ms)

Iter	Nodes	Cost
0	151	1338
1	344	1249
2	1049	1130
3	4786	1101
done	5000	1101

prune398.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.3b

regimes201.0ms

Accuracy

43.4% (3.9b remaining)

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

bsearch77.0ms

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

sample3.2s

Algorithm

intervals

Results

759.0ms	1490×	body	10240	exit
756.0ms	1406×	body	1280	valid
491.0ms	1612×	body	640	valid
222.0ms	3515×	body	80	valid
172.0ms	903×	body	320	valid
115.0ms	84×	body	2560	valid
95.0ms	2485×	body	80	nan
58.0ms	502×	body	160	valid
56.0ms	264×	body	640	nan
32.0ms	104×	body	1280	nan
28.0ms	197×	body	320	nan
10.0ms	115×	body	160	nan