Details

sample615.0ms

Algorithm

intervals

Results

154.0ms	53×	body	10240	exit
40.0ms	33×	body	1280	valid
32.0ms	41×	body	640	valid
22.0ms	131×	body	80	valid
22.0ms	33×	body	320	valid
12.0ms	89×	body	80	nan
5.0ms	2×	body	2560	valid
4.0ms	16×	body	160	valid
2.0ms	4×	body	640	nan
1.0ms	2×	body	1280	nan
1.0ms	4×	body	160	nan
1.0ms	2×	body	320	nan

simplify37.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
23	4994
22	4972
21	4957
20	4939
19	4922
18	4900
17	4883
16	4867
15	4850
14	4820
13	4503
12	3428
11	2838
10	1851
9	1170
8	866
7	560
6	285
5	127
4	77
3	53
2	35
1	20
0	12

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (expm1 z) y 1.0)
0.0b	(expm1 z)
0.0b	(/ (log (fma (expm1 z) y 1.0)) t)
4.3b	(log (fma (expm1 z) y 1.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

1.0ms	(fma (expm1 z) y 1.0)
1.0ms	(expm1 z)
16.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
12.0ms	(log (fma (expm1 z) y 1.0))

series2.3s

Counts

4 → 12

Calls

4 calls:

143.0ms	(fma (expm1 z) y 1.0)
117.0ms	(expm1 z)
1.4s	(/ (log (fma (expm1 z) y 1.0)) t)
679.0ms	(log (fma (expm1 z) y 1.0))

simplify13.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	5023
3	3191
2	1003
1	351
0	162

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))))
4.3b	(log (fma (expm1 z) y 1.0))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
63×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`pow1`
20×	`associate-/r*`
18×	`add-exp-log`
17×	`log-pow`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `rem-log-exp` `associate-/r/` `fma-udef` `inv-pow`

Counts

4 → 147

Calls

4 calls:

1.0ms	(fma (expm1 z) y 1.0)
13.0ms	(/ t (log (fma (expm1 z) y 1.0)))
46.0ms	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
3.0ms	(log (fma (expm1 z) y 1.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

395.0ms	(fma (expm1 z) y 1.0)
912.0ms	(/ t (log (fma (expm1 z) y 1.0)))
348.0ms	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
304.0ms	(log (fma (expm1 z) y 1.0))

simplify11.7s

Counts

159 → 159

Iterations

Iter	Nodes
done	5007
2	2172
1	712
0	283

prune3.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (expm1 z) y 1.0))
0.0b	(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
4.3b	(log (sqrt (fma (expm1 z) y 1.0)))
4.3b	(log (sqrt (fma (expm1 z) y 1.0)))

rewrite161.0ms

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:

3.0ms	(sqrt (fma (expm1 z) y 1.0))
126.0ms	(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
4.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
5.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

series3.5s

Counts

4 → 12

Calls

4 calls:

397.0ms	(sqrt (fma (expm1 z) y 1.0))
2.4s	(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
318.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
408.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

simplify11.9s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
2	3275
1	987
0	375

prune5.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize116.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (sqrt (fma (expm1 z) y 1.0)))
0.9b	(expm1 (log1p (sqrt (fma (expm1 z) y 1.0))))
4.3b	(log (sqrt (fma (expm1 z) y 1.0)))
47.5b	(log (expm1 (log1p (sqrt (fma (expm1 z) y 1.0)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

1.0ms	(log1p (sqrt (fma (expm1 z) y 1.0)))
1.0ms	(expm1 (log1p (sqrt (fma (expm1 z) y 1.0))))
5.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
3.0ms	(log (expm1 (log1p (sqrt (fma (expm1 z) y 1.0)))))

series8.0s

Counts

4 → 12

Calls

4 calls:

2.1s	(log1p (sqrt (fma (expm1 z) y 1.0)))
1.6s	(expm1 (log1p (sqrt (fma (expm1 z) y 1.0))))
987.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
3.3s	(log (expm1 (log1p (sqrt (fma (expm1 z) y 1.0)))))

simplify16.3s

Counts

67 → 67

Iterations

Iter	Nodes
done	5013
2	3509
1	959
0	331

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

regimes2.0s

Accuracy

43.7% (4.4b remaining)

Error of 8.1b against oracle of 3.7b and baseline of 11.5b

bsearch543.0ms

Steps

Iters	Range		Point
9	-1.639266218632692e-61	-2.4289870293945252e-67	-4.8564381873851215e-65

simplify28.0ms

Iterations

Iter	Nodes
done	37
1	37
0	34

end0.0ms

sample38.9s

Algorithm

intervals

Results

15.6s	1486×	body	10240	exit
9.6s	1470×	body	1280	valid
3.3s	1547×	body	640	valid
1.9s	3503×	body	80	valid
1.8s	927×	body	320	valid
1.4s	480×	body	160	valid
1.4s	101×	body	1280	nan
994.0ms	2456×	body	80	nan
985.0ms	242×	body	640	nan
444.0ms	98×	body	2560	valid
210.0ms	193×	body	320	nan
33.0ms	115×	body	160	nan