Details

sample191.0ms

Algorithm

intervals

Results

52.0ms	49×	body	10240	exit
31.0ms	64×	body	640	valid
30.0ms	42×	body	1280	valid
11.0ms	111×	body	80	valid
8.0ms	25×	body	320	valid
7.0ms	103×	body	80	nan
5.0ms	13×	body	640	nan
4.0ms	3×	body	2560	valid
3.0ms	15×	body	160	valid
2.0ms	10×	body	320	nan
2.0ms	4×	body	1280	nan
0.0ms	2×	body	160	nan

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 10 (476.0ms)

Iter	Nodes	Cost
0	12	13
1	20	13
2	35	12
3	53	12
4	77	12
5	106	12
6	138	12
7	176	12
8	232	12
9	295	12
10	459	10
11	498	10
12	500	10
done	500	10

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ (log (fma (expm1 z) y 1.0)) t))
0.0b	(/ (log (fma (expm1 z) y 1.0)) t)
5.2b	(log (fma (expm1 z) y 1.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`add-cube-cbrt`
49×	`times-frac`
48×	`prod-diff`
17×	`pow1`
14×	`log-pow`
6×	`add-exp-log`
5×	`add-cbrt-cube` `add-log-exp`
4×	`div-inv` `associate-/l*`
3×	`expm1-log1p-u` `log-prod` `fma-neg` `associate-/r*` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip--` `distribute-lft-out--`

Counts

3 → 115

Calls

3 calls:

20.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
15.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
3.0ms	(log (fma (expm1 z) y 1.0))

series410.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
207.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
100.0ms	(log (fma (expm1 z) y 1.0))

simplify1.7s

Counts

124 → 124

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	252	4198
1	580	3760
2	1528	2551
done	5001	2111

prune417.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ 1 (/ t (log (fma (expm1 z) y 1.0)))))
0.1b	(/ t (log (fma (expm1 z) y 1.0)))
0.1b	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
5.2b	(log (fma (expm1 z) y 1.0))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
254×	`add-sqr-sqrt`
245×	`*-un-lft-identity`
240×	`add-cube-cbrt`
159×	`prod-diff`
49×	`pow1`
44×	`log-pow`
20×	`associate-/r*`
19×	`div-inv`
18×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`associate-/l*` `add-log-exp`
5×	`difference-of-squares`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`log-prod` `fma-neg`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `rem-log-exp` `flip--` `inv-pow`

Counts

4 → 320

Calls

4 calls:

70.0ms	(- x (/ 1 (/ t (log (fma (expm1 z) y 1.0)))))
5.0ms	(/ t (log (fma (expm1 z) y 1.0)))
11.0ms	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
2.0ms	(log (fma (expm1 z) y 1.0))

series608.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- x (/ 1 (/ t (log (fma (expm1 z) y 1.0)))))
278.0ms	(/ t (log (fma (expm1 z) y 1.0)))
111.0ms	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
113.0ms	(log (fma (expm1 z) y 1.0))

simplify1.9s

Counts

332 → 332

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	606	16144
1	1497	13134
2	3212	9597
done	5000	8718

prune868.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3)
5.2b	(log (fma (expm1 z) y 1.0))
5.2b	(log (fma (expm1 z) y 1.0))
5.2b	(log (fma (expm1 z) y 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod`
8×	`pow1` `add-exp-log`
6×	`cbrt-prod` `unpow-prod-down` `cube-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `rem-log-exp` `log-pow`
2×	`pow-pow`
1×	`cube-mult` `pow-to-exp` `pow1/3` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

7.0ms	(pow (cbrt t) 3)
3.0ms	(log (fma (expm1 z) y 1.0))
3.0ms	(log (fma (expm1 z) y 1.0))
3.0ms	(log (fma (expm1 z) y 1.0))

series724.0ms

Counts

4 → 12

Calls

4 calls:

396.0ms	(pow (cbrt t) 3)
101.0ms	(log (fma (expm1 z) y 1.0))
112.0ms	(log (fma (expm1 z) y 1.0))
115.0ms	(log (fma (expm1 z) y 1.0))

simplify4.2s

Counts

86 → 86

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	105	905
1	246	751
2	555	667
3	1499	657
4	4989	645
done	5000	642

prune618.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.8b

localize48.0ms

Local error

Found 4 expressions with local error:

5.0b	(log (sqrt (fma (expm1 z) y 1.0)))
5.0b	(log (sqrt (fma (expm1 z) y 1.0)))
5.2b	(log (fma (expm1 z) y 1.0))
5.2b	(log (fma (expm1 z) y 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

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

series672.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
205.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
104.0ms	(log (fma (expm1 z) y 1.0))
110.0ms	(log (fma (expm1 z) y 1.0))

simplify1.8s

Counts

78 → 78

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	198	1718
1	546	1568
2	1820	1434
done	5000	1322

prune747.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.8b

regimes583.0ms

Accuracy

38.6% (4.6b remaining)

Error of 8.8b against oracle of 4.2b and baseline of 11.8b

bsearch133.0ms

Steps

Iters	Range		Point
9	-595411.4635753314	-0.3063967055351801	-0.3115017031960372

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	41
1	30	41
done	30	41

end0.0ms

sample7.5s

Algorithm

intervals

Results

2.1s	1488×	body	1280	valid
1.9s	1449×	body	10240	exit
999.0ms	1615×	body	640	valid
401.0ms	3540×	body	80	valid
336.0ms	873×	body	320	valid
253.0ms	2496×	body	80	nan
177.0ms	73×	body	2560	valid
146.0ms	448×	body	160	valid
100.0ms	257×	body	640	nan
88.0ms	191×	body	320	nan
65.0ms	110×	body	1280	nan
17.0ms	103×	body	160	nan