Details

sample156.0ms

Algorithm

intervals

Results

31.0ms	36×	body	1280	valid
27.0ms	32×	body	10240	exit
23.0ms	51×	body	640	valid
14.0ms	30×	body	320	valid
11.0ms	127×	body	80	valid
6.0ms	2×	body	2560	valid
5.0ms	84×	body	80	nan
3.0ms	8×	body	640	nan
2.0ms	11×	body	160	valid
1.0ms	4×	body	1280	nan
1.0ms	5×	body	320	nan
1.0ms	4×	body	160	nan

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 10 (486.0ms)

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: 11.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ (log (fma (expm1 z) y 1.0)) t))
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
0.2b	(fma (expm1 z) y 1.0)
3.5b	(log (fma (expm1 z) y 1.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

23.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
10.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
0.0ms	(fma (expm1 z) y 1.0)
2.0ms	(log (fma (expm1 z) y 1.0))

series489.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
231.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
63.0ms	(fma (expm1 z) y 1.0)
77.0ms	(log (fma (expm1 z) y 1.0))

simplify1.6s

Counts

137 → 137

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	268	4303
1	616	3861
2	1612	2642
done	5001	2196

prune512.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (expm1 z) y 1.0)
0.2b	(fma (expm1 z) y 1.0)
3.5b	(log (sqrt (fma (expm1 z) y 1.0)))
3.5b	(log (sqrt (fma (expm1 z) y 1.0)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

1.0ms	(fma (expm1 z) y 1.0)
1.0ms	(fma (expm1 z) y 1.0)
5.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
4.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

series621.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(fma (expm1 z) y 1.0)
79.0ms	(fma (expm1 z) y 1.0)
224.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
249.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

simplify1.7s

Counts

70 → 70

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	179	1486
1	503	1356
2	1672	1252
done	5000	1132

prune496.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (expm1 z) y 1.0)
0.2b	(fma (expm1 z) y 1.0)
3.5b	(log (fma (expm1 z) y 1.0))
3.5b	(log (sqrt (fma (expm1 z) y 1.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
7×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log`
4×	`expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`rem-log-exp` `fma-udef`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 53

Calls

4 calls:

0.0ms	(fma (expm1 z) y 1.0)
0.0ms	(fma (expm1 z) y 1.0)
1.0ms	(log (fma (expm1 z) y 1.0))
3.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma (expm1 z) y 1.0)
51.0ms	(fma (expm1 z) y 1.0)
103.0ms	(log (fma (expm1 z) y 1.0))
214.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

simplify2.0s

Counts

65 → 65

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	213	1069
1	581	986
2	1905	899
done	5001	831

prune445.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (expm1 z) y 1.0)
3.5b	(log (sqrt (fma (expm1 z) y 1.0)))
3.5b	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
3.5b	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
21×	`sqrt-prod`
13×	`log-pow`
12×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-pow1`
7×	`add-exp-log`
5×	`pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
1×	`fma-udef`

Counts

4 → 77

Calls

4 calls:

0.0ms	(fma (expm1 z) y 1.0)
2.0ms	(log (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))))

series687.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(fma (expm1 z) y 1.0)
226.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
204.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))
189.0ms	(log (sqrt (sqrt (fma (expm1 z) y 1.0))))

simplify1.8s

Counts

89 → 89

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	233	1553
1	615	1416
2	1948	1302
done	5001	1238

prune486.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.2b

regimes490.0ms

Accuracy

36% (4.6b remaining)

Error of 9.3b against oracle of 4.7b and baseline of 11.9b

bsearch93.0ms

Steps

Iters	Range		Point
8	-1.0254506463579604e-170	-5.115187898543461e-174	-3.731260742038222e-171

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	65
1	31	65
done	31	65

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.2s	1554×	body	10240	exit
1.1s	1421×	body	1280	valid
687.0ms	1571×	body	640	valid
320.0ms	3535×	body	80	valid
265.0ms	960×	body	320	valid
168.0ms	92×	body	2560	valid
133.0ms	2490×	body	80	nan
84.0ms	280×	body	640	nan
73.0ms	444×	body	160	valid
55.0ms	124×	body	1280	nan
37.0ms	188×	body	320	nan
14.0ms	110×	body	160	nan