Details

sample111.0ms

Algorithm

intervals

Results

24.0ms	48×	body	10240	exit
21.0ms	40×	body	1280	valid
20.0ms	57×	body	640	valid
7.0ms	120×	body	80	valid
4.0ms	22×	body	320	valid
3.0ms	3×	body	2560	valid
2.0ms	70×	body	80	nan
2.0ms	11×	body	640	nan
2.0ms	7×	body	1280	nan
1.0ms	14×	body	160	valid
1.0ms	6×	body	320	nan
0.0ms	3×	body	160	nan

simplify646.0ms

Counts

1 → 1

Iterations

Useful iterations: 10 (307.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (log (fma (expm1 z) y 1.0)) t)
3.9b	(log (fma (expm1 z) y 1.0))

rewrite10.0ms

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:

7.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
2.0ms	(log (fma (expm1 z) y 1.0))

series229.0ms

Counts

2 → 6

Calls

2 calls:

156.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
74.0ms	(log (fma (expm1 z) y 1.0))

simplify1.5s

Counts

53 → 53

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	130	750
1	274	718
2	715	656
3	1903	653
done	5001	648

prune189.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

localize16.0ms

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))
3.5b	(log (cbrt (fma (expm1 z) y 1.0)))
3.5b	(log (cbrt (fma (expm1 z) y 1.0)))

rewrite7.0ms

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:

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

series560.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(cbrt (fma (expm1 z) y 1.0))
134.0ms	(cbrt (fma (expm1 z) y 1.0))
144.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
145.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify1.3s

Counts

74 → 74

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	110	1166
1	261	1088
2	696	994
3	2292	950
done	5000	896

prune357.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize23.0ms

Local error

Found 4 expressions with local error:

3.2b	(log (cbrt (exp (* 2 (log (cbrt (fma (expm1 z) y 1.0)))))))
3.2b	(log (cbrt (cbrt (fma (expm1 z) y 1.0))))
3.5b	(log (cbrt (fma (expm1 z) y 1.0)))
3.5b	(log (cbrt (fma (expm1 z) y 1.0)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

51×	`log-prod`
36×	`cbrt-prod`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`exp-sum`
8×	`pow1` `add-exp-log` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `pow1/3` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 87

Calls

4 calls:

8.0ms	(log (cbrt (exp (* 2 (log (cbrt (fma (expm1 z) y 1.0)))))))
3.0ms	(log (cbrt (cbrt (fma (expm1 z) y 1.0))))
2.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
2.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(log (cbrt (exp (* 2 (log (cbrt (fma (expm1 z) y 1.0)))))))
143.0ms	(log (cbrt (cbrt (fma (expm1 z) y 1.0))))
147.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
144.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify855.0ms

Counts

99 → 99

Iterations

Useful iterations: done (851.0ms)

Iter	Nodes	Cost
0	272	1881
1	590	1607
2	1541	1486
done	5000	1446

prune590.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize25.0ms

Local error

Found 4 expressions with local error:

3.2b	(log (cbrt (cbrt (fma (expm1 z) y 1.0))))
3.2b	(log (sqrt (cbrt (pow (cbrt (fma (expm1 z) y 1.0)) 2))))
3.2b	(log (sqrt (cbrt (pow (cbrt (fma (expm1 z) y 1.0)) 2))))
3.5b	(log (cbrt (fma (expm1 z) y 1.0)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

49×	`log-prod`
40×	`cbrt-prod`
28×	`sqrt-prod`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `log-pow`
10×	`pow1`
8×	`add-exp-log`
4×	`expm1-log1p-u` `sqrt-pow1` `pow1/3` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/2` `unpow2` `sqr-pow`

Counts

4 → 101

Calls

4 calls:

3.0ms	(log (cbrt (cbrt (fma (expm1 z) y 1.0))))
6.0ms	(log (sqrt (cbrt (pow (cbrt (fma (expm1 z) y 1.0)) 2))))
7.0ms	(log (sqrt (cbrt (pow (cbrt (fma (expm1 z) y 1.0)) 2))))
6.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(log (cbrt (cbrt (fma (expm1 z) y 1.0))))
153.0ms	(log (sqrt (cbrt (pow (cbrt (fma (expm1 z) y 1.0)) 2))))
146.0ms	(log (sqrt (cbrt (pow (cbrt (fma (expm1 z) y 1.0)) 2))))
147.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify1.4s

Counts

113 → 113

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	201	2073
1	377	1879
2	824	1714
3	2085	1706
done	5000	1682

prune648.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

regimes245.0ms

Accuracy

38% (4.3b remaining)

Error of 8.5b against oracle of 4.3b and baseline of 11.1b

bsearch86.0ms

Steps

Iters	Range		Point
8	-1.1134152590422517e-89	-1.9514106615128284e-94	-1.022726975677261e-92

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	65
1	39	65
done	39	65

end0.0ms

sample3.3s

Algorithm

intervals

Results

766.0ms	1549×	body	10240	exit
733.0ms	1394×	body	1280	valid
447.0ms	1561×	body	640	valid
215.0ms	3585×	body	80	valid
162.0ms	904×	body	320	valid
113.0ms	89×	body	2560	valid
87.0ms	2462×	body	80	nan
57.0ms	285×	body	640	nan
56.0ms	497×	body	160	valid
32.0ms	114×	body	1280	nan
23.0ms	180×	body	320	nan
10.0ms	125×	body	160	nan