Details

sample102.0ms

Algorithm

intervals

Results

25.0ms	49×	body	1280	valid
20.0ms	41×	body	10240	exit
15.0ms	55×	body	640	valid
6.0ms	101×	body	80	valid
6.0ms	31×	body	320	valid
4.0ms	2×	body	2560	valid
3.0ms	72×	body	80	nan
2.0ms	18×	body	160	valid
1.0ms	8×	body	640	nan
1.0ms	4×	body	1280	nan
1.0ms	4×	body	320	nan
0.0ms	3×	body	160	nan

simplify18.4s

Counts

1 → 1

Iterations

Useful iterations: 8 (161.0ms)

Iter	Nodes	Cost
0	12	13
1	20	13
2	35	12
3	51	12
4	78	12
5	134	12
6	204	12
7	288	12
8	477	10
9	719	10
10	885	10
11	934	10
12	1264	10
13	3672	10
done	5000	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.0b

localize9.0ms

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)
3.0b	(log (fma (expm1 z) y 1.0))

rewrite22.0ms

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

Counts

3 → 115

Calls

3 calls:

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

series248.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
125.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
60.0ms	(log (fma (expm1 z) y 1.0))

simplify777.0ms

Counts

124 → 124

Iterations

Useful iterations: done (772.0ms)

Iter	Nodes	Cost
0	252	4198
1	601	3760
2	2009	2551
done	5000	2542

prune318.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.5b

localize12.0ms

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))
3.1b	(log (cbrt (fma (expm1 z) y 1.0)))
3.1b	(log (cbrt (fma (expm1 z) y 1.0)))

rewrite4.0ms

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:

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

series461.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(cbrt (fma (expm1 z) y 1.0))
110.0ms	(cbrt (fma (expm1 z) y 1.0))
117.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
122.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify1.4s

Counts

74 → 74

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	110	1166
1	262	1090
2	818	994
3	3787	946
done	5000	944

prune352.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/3 (log (fma (expm1 z) y 1.0)))
0.1b	(cbrt (fma (expm1 z) y 1.0))
3.0b	(log (fma (expm1 z) y 1.0))
3.1b	(log (cbrt (fma (expm1 z) y 1.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

15×	`log-prod`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`add-exp-log`
6×	`cbrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
2×	`pow1/3` `rem-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

7.0ms	(* 1/3 (log (fma (expm1 z) y 1.0)))
0.0ms	(cbrt (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* 1/3 (log (fma (expm1 z) y 1.0)))
113.0ms	(cbrt (fma (expm1 z) y 1.0))
63.0ms	(log (fma (expm1 z) y 1.0))
118.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify457.0ms

Counts

84 → 84

Iterations

Useful iterations: done (455.0ms)

Iter	Nodes	Cost
0	172	1242
1	399	1165
2	1344	1034
done	5001	1017

prune408.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fma (expm1 z) y 1.0))
0.1b	(* (sqrt (cbrt (fma (expm1 z) y 1.0))) (sqrt (cbrt (fma (expm1 z) y 1.0))))
3.0b	(log (fma (expm1 z) y 1.0))
3.1b	(log (* (sqrt (cbrt (fma (expm1 z) y 1.0))) (sqrt (cbrt (fma (expm1 z) y 1.0)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`sqrt-prod`
36×	`pow1`
28×	`sqrt-pow1`
21×	`cbrt-prod`
18×	`add-cube-cbrt` `*-un-lft-identity` `log-pow`
16×	`pow1/2`
13×	`pow1/3`
12×	`pow-prod-up`
11×	`swap-sqr`
10×	`add-exp-log`
9×	`associate-r` `associate-l` `unswap-sqr`
8×	`pow-prod-down` `pow-sqr`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log-prod` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
2×	`pow2` `pow-plus` `prod-exp`
1×	`sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

0.0ms	(cbrt (fma (expm1 z) y 1.0))
11.0ms	(* (sqrt (cbrt (fma (expm1 z) y 1.0))) (sqrt (cbrt (fma (expm1 z) y 1.0))))
1.0ms	(log (fma (expm1 z) y 1.0))
6.0ms	(log (* (sqrt (cbrt (fma (expm1 z) y 1.0))) (sqrt (cbrt (fma (expm1 z) y 1.0)))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (fma (expm1 z) y 1.0))
118.0ms	(* (sqrt (cbrt (fma (expm1 z) y 1.0))) (sqrt (cbrt (fma (expm1 z) y 1.0))))
59.0ms	(log (fma (expm1 z) y 1.0))
124.0ms	(log (* (sqrt (cbrt (fma (expm1 z) y 1.0))) (sqrt (cbrt (fma (expm1 z) y 1.0)))))

simplify824.0ms

Counts

136 → 136

Iterations

Useful iterations: 2 (167.0ms)

Iter	Nodes	Cost
0	192	2473
1	423	1753
2	1832	1577
done	5001	1577

prune505.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.5b

regimes323.0ms

Accuracy

44.1% (3.9b remaining)

Error of 8.0b against oracle of 4.1b and baseline of 11.0b

bsearch39.0ms

Steps

Iters	Range		Point
4	-1.835471523199371e-27	-1.0306700494205176e-27	-1.052384401893189e-27

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	46
1	36	46
done	36	46

end0.0ms

sample3.1s

Algorithm

intervals

Results

764.0ms	1567×	body	10240	exit
742.0ms	1438×	body	1280	valid
471.0ms	1643×	body	640	valid
211.0ms	3542×	body	80	valid
155.0ms	880×	body	320	valid
93.0ms	69×	body	2560	valid
91.0ms	2490×	body	80	nan
63.0ms	301×	body	640	nan
50.0ms	458×	body	160	valid
31.0ms	107×	body	1280	nan
25.0ms	188×	body	320	nan
9.0ms	115×	body	160	nan