Details

sample289.0ms

Algorithm

intervals

Results

62.0ms	50×	body	1280	valid
62.0ms	49×	body	10240	exit
44.0ms	39×	body	320	valid
38.0ms	49×	body	640	valid
17.0ms	6×	body	2560	valid
16.0ms	100×	body	80	valid
9.0ms	75×	body	80	nan
5.0ms	7×	body	1280	nan
4.0ms	13×	body	160	valid
3.0ms	6×	body	320	nan
2.0ms	4×	body	640	nan
1.0ms	2×	body	160	nan

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
11	1735
10	1206
9	788
8	572
7	448
6	253
5	127
4	77
3	53
2	35
1	20
0	12

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.6b

localize41.0ms

Local error

Found 3 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)
3.9b	(log (fma (expm1 z) y 1.0))

rewrite34.0ms

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` `associate-/r*` `fma-neg` `insert-posit16` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `rem-log-exp` `flip--` `distribute-lft-out--`

Counts

3 → 118

Calls

3 calls:

16.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
13.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
3.0ms	(log (fma (expm1 z) y 1.0))

series389.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
171.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
113.0ms	(log (fma (expm1 z) y 1.0))

simplify894.0ms

Counts

127 → 127

Iterations

Iter	Nodes
done	2005
2	1671
1	619
0	253

prune588.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (fma (expm1 z) y 1.0)) (log (fma (expm1 z) y 1.0)))
3.9b	(log (fma (expm1 z) y 1.0))
3.9b	(log (fma (expm1 z) y 1.0))
3.9b	(log (fma (expm1 z) y 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
15×	`add-sqr-sqrt` `log-prod` `*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`add-exp-log` `log-pow`
6×	`add-cbrt-cube` `swap-sqr`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `rem-log-exp`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

13.0ms	(* (log (fma (expm1 z) y 1.0)) (log (fma (expm1 z) y 1.0)))
2.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))

series332.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (log (fma (expm1 z) y 1.0)) (log (fma (expm1 z) y 1.0)))
68.0ms	(log (fma (expm1 z) y 1.0))
82.0ms	(log (fma (expm1 z) y 1.0))
77.0ms	(log (fma (expm1 z) y 1.0))

simplify1.0s

Counts

96 → 96

Iterations

Iter	Nodes
done	2001
2	1430
1	434
0	143

prune503.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.0b

localize40.0ms

Local error

Found 4 expressions with local error:

3.7b	(log (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0))))
3.7b	(log (cbrt (fma (expm1 z) y 1.0)))
3.9b	(log (fma (expm1 z) y 1.0))
3.9b	(log (fma (expm1 z) y 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1`
13×	`log-prod` `log-pow`
10×	`add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`pow1/3`
5×	`rem-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp`

Counts

4 → 71

Calls

4 calls:

6.0ms	(log (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0))))
2.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))

series436.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(log (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0))))
139.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
65.0ms	(log (fma (expm1 z) y 1.0))
74.0ms	(log (fma (expm1 z) y 1.0))

simplify826.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	2003
2	1451
1	450
0	179

prune718.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.0b

localize56.0ms

Local error

Found 4 expressions with local error:

3.7b	(log (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0))))
3.9b	(log (fma (expm1 z) y 1.0))
3.9b	(log (fma (expm1 z) y 1.0))
3.9b	(log (fma (expm1 z) y 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1`
12×	`log-pow`
10×	`log-prod` `add-exp-log`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1/3`
5×	`rem-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp`

Counts

4 → 67

Calls

4 calls:

6.0ms	(log (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0))))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))

series409.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(log (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0))))
88.0ms	(log (fma (expm1 z) y 1.0))
90.0ms	(log (fma (expm1 z) y 1.0))
73.0ms	(log (fma (expm1 z) y 1.0))

simplify660.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	2004
2	1187
1	360
0	138

prune608.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.0b

regimes763.0ms

Accuracy

43.8% (4.0b remaining)

Error of 8.7b against oracle of 4.7b and baseline of 11.8b

bsearch187.0ms

Steps

Iters	Range		Point
9	-4.379888677802055e-76	-8.274282137732009e-83	-3.001899740921049e-81

simplify7.0ms

Iterations

Iter	Nodes
done	25
1	25
0	23

end0.0ms

sample8.7s

Algorithm

intervals

Results

2.2s	1445×	body	1280	valid
2.1s	1491×	body	10240	exit
1.3s	1592×	body	640	valid
712.0ms	2492×	body	80	nan
667.0ms	3467×	body	80	valid
529.0ms	914×	body	320	valid
244.0ms	97×	body	2560	valid
153.0ms	515×	body	160	valid
129.0ms	232×	body	640	nan
114.0ms	172×	body	320	nan
75.0ms	98×	body	1280	nan
29.0ms	122×	body	160	nan