Details

analyze10.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
81.2%	18.7%	0%	6
100%	0%	0%	7

Compiler

Compiled 174 to 47 computations (73% saved)

sample44.0ms (1%)

Algorithm

1×

intervals

Results

32.0ms

256×

body

128

valid

Compiler

Compiled 347 to 94 computations (72.9% saved)

simplify241.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4944	106
1	4944	106

prune19.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 31.6b

Counts

2 → 2

Compiler

Compiled 559 to 263 computations (53% saved)

localize46.0ms (1.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 3782789308857969/36028797018963968 (.f64 x x))
0.2b	(.f64 (.f64 x x) 1737369620307813/2251799813685248)
14.4b	(.f64 x (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (.f64 825478423409049/2305843009213693952 (pow.f64 x 12)))))
31.1b	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (*.f64 825478423409049/2305843009213693952 (pow.f64 x 12))))

rewrite117.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_1821`
22×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
21×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
19×	`times-frac_binary64_1805` `associate-r_binary64_1739`
16×	`pow1_binary64_1860`
8×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
7×	`associate-l_binary64_1740` `pow-prod-down_binary64_1870`
4×	`add-log-exp_binary64_1838` `unswap-sqr_binary64_1767` `associate-/r/_binary64_1745`
3×	`associate-/l_binary64_1744` `associate-/r_binary64_1743` `*-commutative_binary64_1730` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833` `associate-/l/_binary64_1746` `div-inv_binary64_1796`
1×	`clear-num_binary64_1798` `frac-2neg_binary64_1810` `associate-*r/_binary64_1741`

Counts

4 → 103

Calls

4 calls:

38.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (*.f64 825478423409049/2305843009213693952 (pow.f64 x 12))))
34.0ms	(.f64 x (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (.f64 825478423409049/2305843009213693952 (pow.f64 x 12)))))
12.0ms	(.f64 3782789308857969/36028797018963968 (.f64 x x))
7.0ms	(.f64 (.f64 x x) 1737369620307813/2251799813685248)

series475.0ms (11.2%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(.f64 x (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (.f64 825478423409049/2305843009213693952 (pow.f64 x 12)))))
177.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (*.f64 825478423409049/2305843009213693952 (pow.f64 x 12))))
36.0ms	(.f64 3782789308857969/36028797018963968 (.f64 x x))
34.0ms	(.f64 (.f64 x x) 1737369620307813/2251799813685248)

simplify107.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5244	8726

prune1.0s (24.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	115	2	117

Merged error: 0b

Counts

117 → 2

Compiler

Compiled 15008 to 11444 computations (23.7% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b

(+.f64 (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5)) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))

0.1b

(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))

0.2b

(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

rewrite78.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`times-frac_binary64_1805`
50×	`*-un-lft-identity_binary64_1799`
44×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834`
24×	`unpow-prod-down_binary64_1878`
19×	`associate-/r*_binary64_1743`
13×	`add-exp-log_binary64_1837`
12×	`cube-prod_binary64_1827`
8×	`sqr-pow_binary64_1771`
7×	`add-cbrt-cube_binary64_1835`
6×	`div-exp_binary64_1850` `associate-/l*_binary64_1744`
5×	`add-log-exp_binary64_1838`
4×	`cube-mult_binary64_1829` `unpow3_binary64_1865`
3×	`pow1_binary64_1860`
2×	`clear-num_binary64_1798` `pow-to-exp_binary64_1868` `frac-2neg_binary64_1810` `cbrt-undiv_binary64_1833` `pow-exp_binary64_1867` `div-inv_binary64_1796` `distribute-lft-out_binary64_1750`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `flip3-+_binary64_1802` `frac-add_binary64_1807` `flip-+_binary64_1773`

Counts

3 → 124

Calls

3 calls:

52.0ms

(+.f64 (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5)) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))

6.0ms

(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

5.0ms

(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))

series296.0ms (7%)

Counts

3 → 9

Calls

3 calls:

178.0ms

(+.f64 (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5)) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))

72.0ms

(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))

46.0ms

(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

simplify75.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4978	1874
1	4978	1874

prune169.0ms (4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	133	2	135

Merged error: 0b

Counts

135 → 2

Compiler

Compiled 2755 to 2168 computations (21.3% saved)

regimes41.0ms (1%)

Compiler: Compiled 88 to 72 computations (18.2% saved)

bsearch159.0ms (3.8%)

Steps

Iters	Range		Point
11	1.2038172487208293e-18	22789.1243024172	802.3089758624382
11	-1.3028368697939755e+42	-1.3220785642623547e+22	-2.234618570849563e+24

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	97	142
1	97	142

end0.0ms (0%)

sample1.3s (31%)

Algorithm

1×

intervals

Results

1.0s

8000×

body

128

valid

Compiler

Compiled 355 to 194 computations (45.4% saved)

Details

analyze10.0ms (0.2%)

sample44.0ms (1%)

simplify241.0ms (5.7%)

prune19.0ms (0.4%)

localize46.0ms (1.1%)

rewrite117.0ms (2.8%)

series475.0ms (11.2%)

simplify107.0ms (2.5%)

prune1.0s (24.2%)

localize14.0ms (0.3%)

rewrite78.0ms (1.9%)

series296.0ms (7%)

simplify75.0ms (1.8%)

prune169.0ms (4%)

regimes41.0ms (1%)

bsearch159.0ms (3.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (31%)

Profiling