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)

sample41.0ms (0.9%)

Algorithm

1×

intervals

Results

29.0ms

256×

body

128

valid

Compiler

Compiled 347 to 94 computations (72.9% saved)

simplify238.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4944	106
1	4944	106

prune8.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 27.6b

Counts

2 → 1

Compiler

Compiled 142 to 114 computations (19.7% saved)

localize173.0ms (3.7%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 3782789308857969/36028797018963968 (.f64 x x))
0.2b	(*.f64 825478423409049/2305843009213693952 (pow.f64 x 12))
14.0b	(.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)))))
26.9b	(/.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))))

rewrite115.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_3510`
24×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
23×	`associate-r_binary64_3428`
21×	`add-exp-log_binary64_3526`
19×	`times-frac_binary64_3494`
18×	`add-cbrt-cube_binary64_3524`
11×	`pow1_binary64_3549`
9×	`associate-l_binary64_3429`
8×	`prod-exp_binary64_3537`
6×	`unswap-sqr_binary64_3456` `cbrt-unprod_binary64_3521`
4×	`associate-/r/_binary64_3434` `unpow-prod-down_binary64_3567` `pow-prod-down_binary64_3559` `add-log-exp_binary64_3527`
3×	`associate-/r_binary64_3432` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/l_binary64_3433` `*-commutative_binary64_3419`
2×	`associate-/l/_binary64_3435` `sqr-pow_binary64_3460` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485`
1×	`pow-exp_binary64_3556` `clear-num_binary64_3487` `pow-to-exp_binary64_3557` `associate-*r/_binary64_3430` `frac-2neg_binary64_3499`

Counts

4 → 109

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)))))
7.0ms	(.f64 3782789308857969/36028797018963968 (.f64 x x))
6.0ms	(*.f64 825478423409049/2305843009213693952 (pow.f64 x 12))

series512.0ms (11%)

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)))))
175.0ms	(/.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))))
75.0ms	(*.f64 825478423409049/2305843009213693952 (pow.f64 x 12))
33.0ms	(.f64 3782789308857969/36028797018963968 (.f64 x x))

simplify103.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5133	8822

prune807.0ms (17.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	120	2	122

Merged error: 0b

Counts

122 → 2

Compiler

Compiled 11376 to 8888 computations (21.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5)) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))
0.0b	(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5)) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))))
0.2b	(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))
0.3b	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

rewrite144.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`times-frac_binary64_3494` `*-un-lft-identity_binary64_3488`
45×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523`
24×	`unpow-prod-down_binary64_3567`
19×	`associate-/r*_binary64_3432`
14×	`add-exp-log_binary64_3526`
12×	`cube-prod_binary64_3516`
11×	`add-log-exp_binary64_3527`
8×	`add-cbrt-cube_binary64_3524` `sqr-pow_binary64_3460`
7×	`distribute-lft-out_binary64_3439`
6×	`associate-/l*_binary64_3433` `div-exp_binary64_3539`
5×	`frac-add_binary64_3496`
4×	`unpow3_binary64_3554` `cube-mult_binary64_3518` `sum-log_binary64_3579` `pow1_binary64_3549`
3×	`flip-+_binary64_3462` `flip3-+_binary64_3491`
2×	`pow-exp_binary64_3556` `clear-num_binary64_3487` `+-commutative_binary64_3418` `pow-to-exp_binary64_3557` `frac-2neg_binary64_3499` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485`
1×	`associate-+r+_binary64_3420`

Counts

4 → 143

Calls

4 calls:

65.0ms	(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5)) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))))
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))

series324.0ms (7%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(+.f64 (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5)) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))
59.0ms	(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))
48.0ms	(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5)) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))))
47.0ms	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

simplify116.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4926	2581
1	4926	2581

prune198.0ms (4.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	155	2	157

Merged error: 0b

Counts

157 → 2

Compiler

Compiled 3307 to 2610 computations (21.1% saved)

regimes134.0ms (2.9%)

Compiler: Compiled 1464 to 808 computations (44.8% saved)

bsearch148.0ms (3.2%)

Steps

Iters	Range		Point
10	18337591.88739643	9.988094580032433e+22	32456945.86867493
11	-1.202408417670608e+30	-59811432372.43635	-3.529822938393265e+16

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	97	142
1	97	142

end0.0ms (0%)

sample1.6s (33.5%)

Algorithm

1×

intervals

Results

944.0ms

8000×

body

128

valid

Compiler

Compiled 827 to 481 computations (41.8% saved)

Details

analyze10.0ms (0.2%)

sample41.0ms (0.9%)

simplify238.0ms (5.1%)

prune8.0ms (0.2%)

localize173.0ms (3.7%)

rewrite115.0ms (2.5%)

series512.0ms (11%)

simplify103.0ms (2.2%)

prune807.0ms (17.4%)

localize14.0ms (0.3%)

rewrite144.0ms (3.1%)

series324.0ms (7%)

simplify116.0ms (2.5%)

prune198.0ms (4.3%)

regimes134.0ms (2.9%)

bsearch148.0ms (3.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (33.5%)

Profiling