Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample59.0ms

Algorithm

intervals

Results

36.0ms	134×	body	160	valid
15.0ms	122×	body	80	valid

simplify97.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5416	83

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.8b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
0.2b	(.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496)))))))))
0.4b	(+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))
14.6b	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_1837`
21×	`*-un-lft-identity_binary64_1852`
20×	`add-cube-cbrt_binary64_1823` `times-frac_binary64_1847`
17×	`add-exp-log_binary64_1816`
15×	`associate-l_binary64_1912`
11×	`add-cbrt-cube_binary64_1824`
8×	`add-log-exp_binary64_1817`
7×	`pow1_binary64_1794`
5×	`flip-+_binary64_1877` `flip3-+_binary64_1850`
4×	`prod-exp_binary64_1799` `div-exp_binary64_1801` `associate-/r/_binary64_1917`
3×	`associate-/l_binary64_1916` `unswap-sqr_binary64_1880` `associate-r_binary64_1911` `associate-/r_binary64_1915`
2×	`distribute-lft-in_binary64_1894` `cbrt-unprod_binary64_1821` `frac-times_binary64_1844` `rec-exp_binary64_1800` `cbrt-undiv_binary64_1822` `distribute-rgt-in_binary64_1895` `associate-*r/_binary64_1913` `1-exp_binary64_1812` `associate-+r+_binary64_1903` `div-inv_binary64_1853`
1×	`clear-num_binary64_1855` `sub-neg_binary64_1856` `pow-prod-down_binary64_1775` `flip3--_binary64_1851` `diff-log_binary64_1763` `associate-l/_binary64_1914` `+-commutative_binary64_1919` `sum-log_binary64_1762` `inv-pow_binary64_1770` `pow-flip_binary64_1778` `-commutative_binary64_1920` `frac-2neg_binary64_1845` `flip--_binary64_1878`

Counts

4 → 100

Calls

4 calls:

7.0ms	(/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
16.0ms	(.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496)))))))))
5.0ms	(+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))
5.0ms	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
102.0ms	(.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496)))))))))
90.0ms	(+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))
141.0ms	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	724	2874
1	724	2874
0	724	2874
1	724	2874
0	1	3
1	1	3
0	368	2553
1	368	2553
0	368	2553
1	368	2553
0	1	3
1	1	3
0	413	2721
1	413	2721
0	413	2721
1	413	2721
0	1	3
1	1	3
0	196	1986
1	196	1986
0	196	1986
1	196	1986
0	1	3
1	1	3

simplify189.0ms

Counts

112 → 112

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	4949	6377
1	4949	6377

prune411.0ms

Filtered

79 candidates to 112 candidates (-41.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	7	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	7	113

Merged error: 14.7b

Counts

113 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
0.2b	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
0.2b	(.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))) (/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))))
14.6b	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))) (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))) (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

62×	`frac-times_binary64_1844`
48×	`frac-add_binary64_1842`
46×	`associate-*r/_binary64_1913`
45×	`flip-+_binary64_1877` `flip3-+_binary64_1850`
35×	`add-sqr-sqrt_binary64_1837`
29×	`associate-l/_binary64_1914` `times-frac_binary64_1847` `-un-lft-identity_binary64_1852`
28×	`add-cube-cbrt_binary64_1823`
19×	`add-exp-log_binary64_1816`
15×	`associate-l_binary64_1912`
13×	`add-cbrt-cube_binary64_1824`
7×	`pow1_binary64_1794`
6×	`associate-/l_binary64_1916` `add-log-exp_binary64_1817` `associate-/r_binary64_1915` `associate-/r/_binary64_1917`
5×	`div-exp_binary64_1801`
4×	`prod-exp_binary64_1799` `un-div-inv_binary64_1854`
3×	`cbrt-undiv_binary64_1822` `unswap-sqr_binary64_1880` `associate-r_binary64_1911` `div-inv_binary64_1853`
2×	`clear-num_binary64_1855` `cbrt-unprod_binary64_1821` `rec-exp_binary64_1800` `1-exp_binary64_1812` `frac-2neg_binary64_1845`
1×	`distribute-lft-in_binary64_1894` `sub-neg_binary64_1856` `pow-prod-down_binary64_1775` `flip3--_binary64_1851` `diff-log_binary64_1763` `distribute-rgt-in_binary64_1895` `inv-pow_binary64_1770` `pow-flip_binary64_1778` `*-commutative_binary64_1920` `flip--_binary64_1878`

Counts

4 → 164

Calls

4 calls:

7.0ms	(/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
6.0ms	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
34.0ms	(.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))) (/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))))
5.0ms	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))) (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))) (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))

series433.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
62.0ms	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
133.0ms	(.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))) (/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))))
177.0ms	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))) (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))) (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	1075	2997
1	1075	2997
0	1075	2997
1	1075	2997
0	1	3
1	1	3
0	764	2844
1	764	2844
0	764	2844
1	764	2844
0	1	3
1	1	3
0	203	1986
1	203	1986
0	203	1986
1	203	1986
0	1	3
1	1	3
0	196	1986
1	196	1986
0	196	1986
1	196	1986
0	1	3
1	1	3

simplify235.0ms

Counts

176 → 176

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5025	16500

prune1.0s

Filtered

128 candidates to 176 candidates (-37.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	171	5	176
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	174	9	183

Merged error: 14.6b

Counts

183 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))
0.2b	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
14.6b	(-.f64 1 (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

132×	`*-un-lft-identity_binary64_1852`
109×	`times-frac_binary64_1847`
107×	`add-sqr-sqrt_binary64_1837`
61×	`add-cube-cbrt_binary64_1823`
53×	`sqrt-prod_binary64_1831`
39×	`distribute-lft-out_binary64_1896`
36×	`associate-r_binary64_1911`
30×	`add-exp-log_binary64_1816`
24×	`associate-l_binary64_1912`
20×	`add-cbrt-cube_binary64_1824`
15×	`unswap-sqr_binary64_1880`
10×	`div-exp_binary64_1801`
9×	`associate-/r*_binary64_1915`
8×	`associate-/l*_binary64_1916` `prod-exp_binary64_1799` `associate-/r/_binary64_1917`
6×	`pow1_binary64_1794` `flip-+_binary64_1877` `add-log-exp_binary64_1817` `sqrt-div_binary64_1832` `cbrt-undiv_binary64_1822` `flip3-+_binary64_1850`
4×	`associate-/l/_binary64_1918` `cbrt-unprod_binary64_1821` `div-inv_binary64_1853`
2×	`frac-add_binary64_1842` `clear-num_binary64_1855` `rec-exp_binary64_1800` `1-exp_binary64_1812` `frac-2neg_binary64_1845`
1×	`frac-times_binary64_1844` `sub-neg_binary64_1856` `pow-prod-down_binary64_1775` `flip3--_binary64_1851` `diff-log_binary64_1763` `associate-l/_binary64_1914` `associate-r/_binary64_1913` `*-commutative_binary64_1920` `flip--_binary64_1878`

Counts

4 → 198

Calls

4 calls:

66.0ms	(/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))
7.0ms	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
88.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
5.0ms	(-.f64 1 (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))
65.0ms	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
149.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
172.0ms	(-.f64 1 (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (sqrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	5146	2952
0	5146	2952
0	1	3
1	1	3
0	5076	2799
0	5076	2799
0	1	3
1	1	3
0	203	1986
1	203	1986
0	203	1986
1	203	1986
0	1	3
1	1	3
0	4990	2631
1	4990	2631
0	4990	2631
1	4990	2631
0	1	3
1	1	3

simplify216.0ms

Counts

210 → 210

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5022	18450

prune1.0s

Filtered

120 candidates to 210 candidates (-75.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	210	9	219

Merged error: 14.6b

Counts

219 → 9

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
0.2b	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
0.2b	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
14.6b	(-.f64 1 (.f64 (/.f64 (/.f64 (-.f64 (.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (.f64 (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (-.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))) (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-cube-cbrt_binary64_1823` `add-sqr-sqrt_binary64_1837` `*-un-lft-identity_binary64_1852`
27×	`times-frac_binary64_1847`
10×	`add-cbrt-cube_binary64_1824` `add-exp-log_binary64_1816`
9×	`associate-/l_binary64_1916` `associate-/r_binary64_1915`
6×	`add-log-exp_binary64_1817` `associate-/r/_binary64_1917`
4×	`pow1_binary64_1794`
3×	`clear-num_binary64_1855` `flip-+_binary64_1877` `cbrt-undiv_binary64_1822` `div-exp_binary64_1801` `flip3-+_binary64_1850` `frac-2neg_binary64_1845` `div-inv_binary64_1853`
1×	`sub-neg_binary64_1856` `flip3--_binary64_1851` `diff-log_binary64_1763` `flip--_binary64_1878`

Counts

4 → 98

Calls

4 calls:

6.0ms	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
6.0ms	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
6.0ms	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
5.0ms	(-.f64 1 (.f64 (/.f64 (/.f64 (-.f64 (.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (.f64 (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (-.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))) (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

series631.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
63.0ms	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
66.0ms	(/.f64 -5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
435.0ms	(-.f64 1 (.f64 (/.f64 (/.f64 (-.f64 (.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (.f64 (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (-.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))) (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4061	3678
1	4061	3678
0	4061	3678
1	4061	3678
0	1	3
1	1	3
0	203	1986
1	203	1986
0	203	1986
1	203	1986
0	1	3
1	1	3
0	203	1986
1	203	1986
0	203	1986
1	203	1986
0	1	3
1	1	3
0	203	1986
1	203	1986
0	203	1986
1	203	1986
0	1	3
1	1	3

simplify164.0ms

Counts

110 → 110

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5347	5198

prune1.2s

Filtered

86 candidates to 110 candidates (-27.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	110	9	119

Merged error: 14.6b

Counts

119 → 9

regimes136.0ms

Accuracy

0% (0.1b remaining)

Error of 13.6b against oracle of 13.6b and baseline of 13.6b

bsearch0.0ms

simplify16.0ms

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	284	111
1	284	111

end0.0ms

sample1.5s

Algorithm

intervals

Results

930.0ms	3857×	body	160	valid
511.0ms	4143×	body	80	valid

Details

analyze2.0ms

sample59.0ms

simplify97.0ms

prune7.0ms

localize23.0ms

rewrite38.0ms

series397.0ms

simplify189.0ms

prune411.0ms

localize24.0ms

rewrite63.0ms

series433.0ms

simplify235.0ms

prune1.0s

localize26.0ms

rewrite179.0ms

series514.0ms

simplify216.0ms

prune1.0s

localize43.0ms

rewrite28.0ms

series631.0ms

simplify164.0ms

prune1.2s

regimes136.0ms

bsearch0.0ms

simplify16.0ms

end0.0ms

sample1.5s

Profiling