Details

sample208.0ms

Algorithm

intervals

Results

47.0ms	51×	body	10240	exit
38.0ms	41×	body	1280	valid
27.0ms	116×	body	80	valid
25.0ms	44×	body	640	valid
12.0ms	34×	body	320	valid
11.0ms	4×	body	2560	valid
7.0ms	87×	body	80	nan
5.0ms	18×	body	160	valid
2.0ms	4×	body	1280	nan
2.0ms	5×	body	640	nan
1.0ms	6×	body	320	nan
0.0ms	3×	body	160	nan

simplify992.0ms

Counts

1 → 1

Iterations

Useful iterations: 10 (478.0ms)

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (expm1 z) y 1.0)
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
4.1b	(log (fma (expm1 z) y 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

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

series356.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(fma (expm1 z) y 1.0)
186.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
104.0ms	(log (fma (expm1 z) y 1.0))

simplify2.1s

Counts

66 → 66

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	146	855
1	310	819
2	802	747
3	2138	738
done	5000	733

prune409.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (expm1 z) y 1.0))
0.1b	(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
4.2b	(log (sqrt (fma (expm1 z) y 1.0)))
4.2b	(log (sqrt (fma (expm1 z) y 1.0)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

94×	`log-pow`
80×	`*-un-lft-identity`
78×	`times-frac`
73×	`pow1`
57×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
40×	`distribute-rgt-out`
32×	`distribute-lft-out`
27×	`sqrt-pow1` `pow1/2`
26×	`associate-/l*`
12×	`log-prod`
9×	`sqrt-prod`
8×	`add-exp-log` `distribute-lft1-in` `distribute-rgt1-in`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `count-2` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`rem-log-exp` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 176

Calls

4 calls:

2.0ms	(sqrt (fma (expm1 z) y 1.0))
60.0ms	(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
2.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
2.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

151.0ms	(sqrt (fma (expm1 z) y 1.0))
850.0ms	(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
207.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
212.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

simplify2.0s

Counts

188 → 188

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	375	4355
1	937	3423
2	2918	3092
done	5000	3069

prune778.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (+ (log (sqrt (sqrt (fma (expm1 z) y 1.0)))) (log (sqrt (sqrt (fma (expm1 z) y 1.0)))))) t)
4.2b	(log (sqrt (fma (expm1 z) y 1.0)))
4.3b	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
4.3b	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
89×	`log-pow`
88×	`distribute-lft-out`
76×	`pow1`
45×	`times-frac`
32×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`log-prod`
21×	`sqrt-pow1` `sqrt-prod`
17×	`pow1/2`
15×	`associate-/l*`
9×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp` `associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 146

Calls

4 calls:

314.0ms	(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (+ (log (sqrt (sqrt (fma (expm1 z) y 1.0)))) (log (sqrt (sqrt (fma (expm1 z) y 1.0)))))) t)
4.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
7.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
5.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (+ (log (sqrt (sqrt (fma (expm1 z) y 1.0)))) (log (sqrt (sqrt (fma (expm1 z) y 1.0)))))) t)
155.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
180.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
205.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))

simplify2.0s

Counts

158 → 158

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	345	4431
1	925	3575
2	3043	3292
done	5001	3278

prune903.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize55.0ms

Local error

Found 4 expressions with local error:

4.3b	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
4.3b	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
4.3b	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
4.3b	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

3.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
3.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
3.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
4.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))

series726.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
188.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
180.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
197.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))

simplify3.2s

Counts

108 → 108

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	93	1620
1	189	1476
2	432	1352
3	1150	1344
4	3681	1316
done	5000	1312

prune647.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

regimes362.0ms

Accuracy

49.2% (3.9b remaining)

Error of 7.6b against oracle of 3.7b and baseline of 11.5b

bsearch225.0ms

Steps

Iters	Range		Point
7	1.497861830149964e-40	2.5310480627793195e-39	5.278878335163117e-40
8	-2.326585084163415e-46	-1.6717231576231503e-49	-6.358797691452859e-48

simplify11.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	49	99
1	54	99
done	54	99

end0.0ms

sample7.1s

Algorithm

intervals

Results

2.0s	1512×	body	10240	exit
1.7s	1494×	body	1280	valid
854.0ms	1493×	body	640	valid
842.0ms	3590×	body	80	valid
349.0ms	874×	body	320	valid
263.0ms	2525×	body	80	nan
169.0ms	84×	body	2560	valid
105.0ms	290×	body	640	nan
100.0ms	502×	body	160	valid
57.0ms	110×	body	1280	nan
45.0ms	183×	body	320	nan
14.0ms	96×	body	160	nan