Details

sample109.0ms

Algorithm

intervals

Results

30.0ms	58×	body	1280	valid
23.0ms	46×	body	10240	exit
15.0ms	53×	body	640	valid
7.0ms	111×	body	80	valid
3.0ms	18×	body	320	valid
2.0ms	63×	body	80	nan
2.0ms	10×	body	640	nan
2.0ms	2×	body	2560	valid
2.0ms	16×	body	160	valid
1.0ms	3×	body	1280	nan
1.0ms	6×	body	320	nan
0.0ms	3×	body	160	nan

simplify618.0ms

Counts

1 → 1

Iterations

Useful iterations: 10 (297.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (expm1 z) y 1.0)
0.0b	(- x (/ (log (fma (expm1 z) y 1.0)) t))
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
4.4b	(log (fma (expm1 z) y 1.0))

rewrite30.0ms

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:

0.0ms	(fma (expm1 z) y 1.0)
16.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
7.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
1.0ms	(log (fma (expm1 z) y 1.0))

series319.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma (expm1 z) y 1.0)
76.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
129.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
68.0ms	(log (fma (expm1 z) y 1.0))

simplify1.3s

Counts

137 → 137

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	268	4303
1	616	3861
2	1612	2642
done	5000	2196

prune338.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ 1 (/ t (log (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))))
4.4b	(log (fma (expm1 z) y 1.0))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
254×	`add-sqr-sqrt`
245×	`*-un-lft-identity`
240×	`add-cube-cbrt`
159×	`prod-diff`
49×	`pow1`
44×	`log-pow`
20×	`associate-/r*`
19×	`div-inv`
18×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`associate-/l*` `add-log-exp`
5×	`difference-of-squares`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`log-prod` `fma-neg`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `rem-log-exp` `flip--` `inv-pow`

Counts

4 → 320

Calls

4 calls:

36.0ms	(- x (/ 1 (/ t (log (fma (expm1 z) y 1.0)))))
6.0ms	(/ t (log (fma (expm1 z) y 1.0)))
11.0ms	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
1.0ms	(log (fma (expm1 z) y 1.0))

series409.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- x (/ 1 (/ t (log (fma (expm1 z) y 1.0)))))
179.0ms	(/ t (log (fma (expm1 z) y 1.0)))
82.0ms	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
69.0ms	(log (fma (expm1 z) y 1.0))

simplify1.2s

Counts

332 → 332

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	606	16144
1	1497	13134
2	3212	9597
done	5000	8718

prune508.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ (/ 1 t) (/ 1 (log (fma (expm1 z) y 1.0)))))
0.1b	(/ 1 (log (fma (expm1 z) y 1.0)))
0.1b	(/ (/ 1 t) (/ 1 (log (fma (expm1 z) y 1.0))))
4.4b	(log (fma (expm1 z) y 1.0))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

2086×	`times-frac`
1145×	`add-sqr-sqrt`
1118×	`*-un-lft-identity`
1110×	`add-cube-cbrt`
639×	`prod-diff`
169×	`pow1`
164×	`log-pow`
123×	`div-inv`
49×	`add-exp-log`
34×	`div-exp`
20×	`associate-/r*`
18×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`difference-of-squares`
9×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`log-prod` `fma-neg`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `rem-log-exp` `flip--` `associate-/l/` `distribute-lft-out--` `inv-pow`

Counts

4 → 989

Calls

4 calls:

102.0ms	(- x (/ (/ 1 t) (/ 1 (log (fma (expm1 z) y 1.0)))))
6.0ms	(/ 1 (log (fma (expm1 z) y 1.0)))
23.0ms	(/ (/ 1 t) (/ 1 (log (fma (expm1 z) y 1.0))))
1.0ms	(log (fma (expm1 z) y 1.0))

series366.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- x (/ (/ 1 t) (/ 1 (log (fma (expm1 z) y 1.0)))))
134.0ms	(/ 1 (log (fma (expm1 z) y 1.0)))
82.0ms	(/ (/ 1 t) (/ 1 (log (fma (expm1 z) y 1.0))))
73.0ms	(log (fma (expm1 z) y 1.0))

simplify1.5s

Counts

1001 → 1001

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	1577	72091
1	4173	53999
done	5001	42796

prune773.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.2b

localize14.0ms

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))
4.4b	(log (cbrt (fma (expm1 z) y 1.0)))
4.4b	(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)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (fma (expm1 z) y 1.0))
118.0ms	(cbrt (fma (expm1 z) y 1.0))
128.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
124.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify1.2s

Counts

74 → 74

Iterations

Useful iterations: done (1.2s)

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

prune327.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.2b

regimes359.0ms

Accuracy

10.6% (6.7b remaining)

Error of 11.1b against oracle of 4.4b and baseline of 11.9b

bsearch228.0ms

Steps

Iters	Range		Point
8	1.0057394993554968e+225	2.673258520161921e+227	2.416944786924906e+225
7	-3.393475176608742e+75	-1.2559300858746215e+74	-1.4453561931716785e+74

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	77
1	42	77
done	42	77

end0.0ms

sample3.2s

Algorithm

intervals

Results

788.0ms	1504×	body	1280	valid
724.0ms	1478×	body	10240	exit
457.0ms	1581×	body	640	valid
208.0ms	3477×	body	80	valid
163.0ms	892×	body	320	valid
96.0ms	2619×	body	80	nan
88.0ms	70×	body	2560	valid
57.0ms	502×	body	160	valid
48.0ms	251×	body	640	nan
30.0ms	102×	body	1280	nan
29.0ms	202×	body	320	nan
9.0ms	108×	body	160	nan