Details

analyze211.0ms (1.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5240	106
0	1	1
1	1	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)

sample50.0ms (0.3%)

Algorithm

1×

intervals

Results

34.0ms

256×

body

128

valid

Compiler

Compiled 347 to 94 computations (72.9% saved)

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5240	106

prune14.0ms (0.1%)

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

Error

29.4b

Counts

2 → 2

Compiler

Compiled 315 to 160 computations (49.2% saved)

localize54.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))
0.3b	(.f64 3782789308857969/36028797018963968 (.f64 x x))
12.9b	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x))))) x)
28.8b	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (*.f64 x x)))))

rewrite4.3s (27.7%)

Algorithm

1×	rewrite-expression-head

Error

29.3b

Rules

369×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
364×	`pow1_binary64_1844`
311×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
310×	`pow-prod-down_binary64_1854`
28×	`add-sqr-sqrt_binary64_1805`
22×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
21×	`associate-l_binary64_1724`
19×	`times-frac_binary64_1789`
5×	`associate-r_binary64_1723`
4×	`add-log-exp_binary64_1822` `associate-/r/_binary64_1729`
3×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-/l_binary64_1728` `associate-/r_binary64_1727` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714`
2×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `div-inv_binary64_1780` `associate-/l/_binary64_1730`
1×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-*l/_binary64_1726`

Counts

4 → 237

Calls

4 calls:

721.0ms	(.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))
95.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (*.f64 x x)))))
84.0ms	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x))))) x)
6.0ms	(.f64 3782789308857969/36028797018963968 (.f64 x x))

Compiler

Compiled 42320 to 9694 computations (77.1% saved)

series860.0ms (5.6%)

Error

0.0b

Counts

4 → 28

Calls

4 calls:

366.0ms	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x))))) x)
298.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (*.f64 x x)))))
99.0ms	(.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))
59.0ms	(.f64 3782789308857969/36028797018963968 (.f64 x x))

Compiler

Compiled 2890 to 1165 computations (59.7% saved)

simplify183.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4984	10117
1	4984	10117

prune832.0ms (5.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	262	3	265
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	264	3	267

Error

0.0b

Counts

267 → 3

Compiler

Compiled 14931 to 6511 computations (56.4% saved)

localize53.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.0b	(sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976))))
12.9b	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (/.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (+.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))))) x)
26.5b	(.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (/.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (+.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)))))
26.9b	(/.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (+.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))))

rewrite2.1s (13.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

53×	`add-sqr-sqrt_binary64_1805`
40×	`times-frac_binary64_1789`
36×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
32×	`sqrt-prod_binary64_1799`
27×	`associate-r_binary64_1723`
20×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
12×	`pow1_binary64_1844` `sqrt-div_binary64_1800`
9×	`associate-*l/_binary64_1726`
8×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
7×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `associate-l_binary64_1724`
6×	`associate-/l*_binary64_1728` `unswap-sqr_binary64_1751`
4×	`add-log-exp_binary64_1822` `associate-/r/_binary64_1729` `pow-prod-down_binary64_1854` `frac-times_binary64_1793`
3×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `associate-/r*_binary64_1727`
2×	`div-inv_binary64_1780` `associate-/l/_binary64_1730` `associate-r/_binary64_1725` `-commutative_binary64_1714`
1×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`

Counts

4 → 137

Calls

4 calls:

54.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (/.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (+.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))))) x)
52.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (/.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (+.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)))))
31.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (+.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	(sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976))))

Compiler

Compiled 20005 to 15729 computations (21.4% saved)

series1.3s (8.1%)

Error

0.0b

Counts

4 → 41

Calls

4 calls:

321.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (+.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))))
320.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (/.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (+.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))))) x)
269.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (/.f64 (sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976)))) (+.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)))))
236.0ms	(sqrt.f64 (+.f64 (.f64 825478423409049/4611686018427387904 (pow.f64 x 10)) (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 3782789308857969/36028797018963968)) (.f64 (pow.f64 x 4) 763919671262763/18014398509481984)) (.f64 (pow.f64 x 6) 8375303961237363/1152921504606846976)) (.f64 (pow.f64 x 8) 583843369866023/1152921504606846976))))

Compiler

Compiled 3949 to 3284 computations (16.8% saved)

simplify238.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4883	19043
1	4883	19043

prune1.4s (9.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	178	3	181

Error

0.0b

Counts

181 → 3

Compiler

Compiled 15683 to 12332 computations (21.4% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))
0.2b	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

rewrite124.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

38×	`times-frac_binary64_1789`
33×	`*-un-lft-identity_binary64_1783`
27×	`add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805`
12×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811` `associate-/r*_binary64_1727`
7×	`add-exp-log_binary64_1821`
4×	`add-log-exp_binary64_1822` `add-cbrt-cube_binary64_1819` `unpow3_binary64_1849` `cube-mult_binary64_1813` `sqr-pow_binary64_1755`
3×	`div-exp_binary64_1834` `associate-/l*_binary64_1728`
2×	`pow1_binary64_1844` `distribute-lft-out_binary64_1734`
1×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `sum-log_binary64_1874` `frac-add_binary64_1791` `flip3-+_binary64_1786` `flip-+_binary64_1757` `+-commutative_binary64_1713`

Counts

2 → 79

Calls

2 calls:

29.0ms	(+.f64 (/.f64 1/2 x) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))
6.0ms	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

Compiler

Compiled 1104 to 876 computations (20.7% saved)

series148.0ms (1%)

Error

0.0b

Counts

2 → 9

Calls

2 calls:

99.0ms	(+.f64 (/.f64 1/2 x) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))
46.0ms	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

Compiler

Compiled 173 to 156 computations (9.8% saved)

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4977	1153
1	4977	1153

prune60.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	88	3	91

Error

0.0b

Counts

91 → 3

Compiler

Compiled 779 to 596 computations (23.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 24015124616067039/36028797018963968 (pow.f64 x 3)))
0.1b	(*.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5))
0.1b	(*.f64 24015124616067039/36028797018963968 (pow.f64 x 3))
19.2b	(+.f64 (.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5)) (-.f64 x (.f64 24015124616067039/36028797018963968 (pow.f64 x 3))))

rewrite167.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

23×	`add-sqr-sqrt_binary64_1805`
19×	`associate-r_binary64_1723`
14×	`add-exp-log_binary64_1821`
11×	`add-log-exp_binary64_1822` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
8×	`add-cbrt-cube_binary64_1819` `unpow-prod-down_binary64_1862`
7×	`unswap-sqr_binary64_1751`
6×	`prod-exp_binary64_1832` `associate-l_binary64_1724`
4×	`pow1_binary64_1844` `cube-prod_binary64_1811` `sqr-pow_binary64_1755`
2×	`diff-log_binary64_1875` `sum-log_binary64_1874` `sub-neg_binary64_1776` `associate-+r+_binary64_1715` `cancel-sign-sub-inv_binary64_1749` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `cbrt-unprod_binary64_1816` `*-commutative_binary64_1714`
1×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-+r-_binary64_1717` `+-commutative_binary64_1713` `unpow3_binary64_1849` `cube-mult_binary64_1813` `flip3--_binary64_1787` `flip--_binary64_1758`

Counts

4 → 83

Calls

4 calls:

9.0ms	(*.f64 24015124616067039/36028797018963968 (pow.f64 x 3))
7.0ms	(+.f64 (.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5)) (-.f64 x (.f64 24015124616067039/36028797018963968 (pow.f64 x 3))))
5.0ms	(*.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5))
3.0ms	(-.f64 x (*.f64 24015124616067039/36028797018963968 (pow.f64 x 3)))

Compiler

Compiled 1553 to 1223 computations (21.2% saved)

series284.0ms (1.8%)

Error

0.0b

Counts

4 → 17

Calls

4 calls:

97.0ms	(-.f64 x (*.f64 24015124616067039/36028797018963968 (pow.f64 x 3)))
66.0ms	(*.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5))
65.0ms	(+.f64 (.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5)) (-.f64 x (.f64 24015124616067039/36028797018963968 (pow.f64 x 3))))
50.0ms	(*.f64 24015124616067039/36028797018963968 (pow.f64 x 3))

Compiler

Compiled 386 to 327 computations (15.3% saved)

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4953	1222
1	4953	1222

prune109.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	100	3	103

Error

Counts

103 → 3

Compiler

Compiled 1237 to 962 computations (22.2% saved)

regimes1.2s (8%)

Accuracy

Total 0.0b remaining (31.2%)

Threshold costs 0.0b (31.2%)

Compiler

Compiled 21011 to 7647 computations (63.6% saved)

bsearch50.0ms (0.3%)

Steps

Iters	Range		Point
1	28.158244862943818	57971954.92993015	40756.661357784425
1	-2415593320909.129	-122398.65168390142	-532326282.4267752

Compiler

Compiled 1 to 1 computations (0% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	95	795
1	95	795

end14.0ms (0.1%)

Compiler: Compiled 530 to 133 computations (74.9% saved)

sample1.5s (9.7%)

Algorithm

1×

intervals

Results

977.0ms

8000×

body

128

valid

Compiler

Compiled 844 to 297 computations (64.8% saved)

Details

analyze211.0ms (1.4%)

sample50.0ms (0.3%)

simplify61.0ms (0.4%)

prune14.0ms (0.1%)

localize54.0ms (0.3%)

rewrite4.3s (27.7%)

series860.0ms (5.6%)

simplify183.0ms (1.2%)

prune832.0ms (5.4%)

localize53.0ms (0.3%)

rewrite2.1s (13.6%)

series1.3s (8.1%)

simplify238.0ms (1.5%)

prune1.4s (9.3%)

localize6.0ms (0%)

rewrite124.0ms (0.8%)

series148.0ms (1%)

simplify58.0ms (0.4%)

prune60.0ms (0.4%)

localize9.0ms (0.1%)

rewrite167.0ms (1.1%)

series284.0ms (1.8%)

simplify54.0ms (0.4%)

prune109.0ms (0.7%)

regimes1.2s (8%)

bsearch50.0ms (0.3%)

simplify8.0ms (0%)

end14.0ms (0.1%)

sample1.5s (9.7%)

Profiling