Details

Time bar (total: 9.7s)

analyze10.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
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)

sample65.0ms (0.7%)

Algorithm
intervals
Results
37.0ms256×body128valid
Compiler

Compiled 347 to 94 computations (72.9% saved)

simplify149.0ms (1.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
05240106

prune22.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
27.9b
Counts
2 → 2
Compiler

Compiled 315 to 160 computations (49.2% saved)

localize42.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.0b
(+.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))
0.0b
(+.f64 (+.f64 1 (*.f64 3782789308857969/36028797018963968 (*.f64 x x))) (*.f64 763919671262763/18014398509481984 (pow.f64 x 4)))
0.0b
(+.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))
0.0b
(+.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)))
0.1b
(*.f64 3782789308857969/36028797018963968 (*.f64 x x))
0.1b
(*.f64 (*.f64 x x) 1737369620307813/2251799813685248)
13.6b
(*.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)))))
27.4b
(/.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))))

rewrite108.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64_2091
22×*-un-lft-identity_binary64_2069 add-cube-cbrt_binary64_2104
21×add-exp-log_binary64_2107 add-cbrt-cube_binary64_2105
19×times-frac_binary64_2075 associate-*r*_binary64_2009
16×pow1_binary64_2130
prod-exp_binary64_2118 cbrt-unprod_binary64_2102
associate-*l*_binary64_2010 pow-prod-down_binary64_2140
add-log-exp_binary64_2108 unswap-sqr_binary64_2037 associate-/r/_binary64_2015
associate-/l*_binary64_2014 flip-+_binary64_2043 *-commutative_binary64_2000 associate-/r*_binary64_2013 flip3-+_binary64_2072
div-inv_binary64_2066 associate-/l/_binary64_2016 cbrt-undiv_binary64_2103 div-exp_binary64_2120
frac-2neg_binary64_2080 associate-*r/_binary64_2011 clear-num_binary64_2068
Counts
4 → 103
Calls

8 calls:

39.0ms
(/.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))))
32.0ms
(*.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 (*.f64 x x) 1737369620307813/2251799813685248)
6.0ms
(*.f64 3782789308857969/36028797018963968 (*.f64 x x))
0.0ms
(+.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)))

series425.0ms (4.4%)

Counts
4 → 26
Calls

4 calls:

182.0ms
(*.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)))))
162.0ms
(/.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))))
41.0ms
(*.f64 (*.f64 x x) 1737369620307813/2251799813685248)
39.0ms
(*.f64 3782789308857969/36028797018963968 (*.f64 x x))
Compiler

Compiled 1196 to 1014 computations (15.2% saved)

simplify142.0ms (1.5%)

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
048998920
148998920

prune952.0ms (9.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1272129
Fresh101
Picked101
Done000
Total1292131
Error
0b
Counts
131 → 2
Compiler

Compiled 11098 to 8668 computations (21.9% saved)

localize46.0ms (0.5%)

Local error

Found 8 expressions with local error:

0.0b
(+.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))
0.0b
(+.f64 (+.f64 1 (*.f64 3782789308857969/36028797018963968 (*.f64 x x))) (*.f64 763919671262763/18014398509481984 (pow.f64 x 4)))
0.0b
(+.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))
0.0b
(+.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)))
0.1b
(*.f64 763919671262763/18014398509481984 (pow.f64 x 4))
0.1b
(*.f64 3782789308857969/36028797018963968 (*.f64 x x))
0.1b
(*.f64 (*.f64 x x) 1737369620307813/2251799813685248)
27.4b
(/.f64 (*.f64 x (+.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))))

rewrite74.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
24×add-exp-log_binary64_2107
21×add-cbrt-cube_binary64_2105
18×add-sqr-sqrt_binary64_2091
14×pow1_binary64_2130
11×*-un-lft-identity_binary64_2069 associate-*r*_binary64_2009 add-cube-cbrt_binary64_2104
10×prod-exp_binary64_2118
cbrt-unprod_binary64_2102
associate-*l*_binary64_2010
pow-prod-down_binary64_2140
unswap-sqr_binary64_2037
add-log-exp_binary64_2108 unpow-prod-down_binary64_2148
*-commutative_binary64_2000 times-frac_binary64_2075 associate-/r*_binary64_2013
associate-*r/_binary64_2011 flip-+_binary64_2043 associate-/l/_binary64_2016 cbrt-undiv_binary64_2103 sqr-pow_binary64_2041 flip3-+_binary64_2072 div-exp_binary64_2120 associate-/r/_binary64_2015
frac-2neg_binary64_2080 div-inv_binary64_2066 clear-num_binary64_2068 associate-/l*_binary64_2014 pow-to-exp_binary64_2138 pow-exp_binary64_2137
Counts
4 → 88
Calls

8 calls:

31.0ms
(/.f64 (*.f64 x (+.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))))
6.0ms
(*.f64 (*.f64 x x) 1737369620307813/2251799813685248)
6.0ms
(*.f64 3782789308857969/36028797018963968 (*.f64 x x))
6.0ms
(*.f64 763919671262763/18014398509481984 (pow.f64 x 4))
0.0ms
(+.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)))

series314.0ms (3.2%)

Counts
4 → 19
Calls

4 calls:

192.0ms
(/.f64 (*.f64 x (+.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))))
46.0ms
(*.f64 763919671262763/18014398509481984 (pow.f64 x 4))
39.0ms
(*.f64 3782789308857969/36028797018963968 (*.f64 x x))
37.0ms
(*.f64 (*.f64 x x) 1737369620307813/2251799813685248)
Compiler

Compiled 1431 to 1188 computations (17% saved)

simplify71.0ms (0.7%)

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
049183788
149183788

prune544.0ms (5.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1070107
Fresh011
Picked011
Done000
Total1072109
Error
0b
Counts
109 → 2
Compiler

Compiled 8035 to 6271 computations (22% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b
(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))
0.0b
(+.f64 (/.f64 1/2 x) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))
0.0b
(+.f64 (/.f64 1/2 x) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))
0.5b
(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

rewrite39.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
38×times-frac_binary64_2075
33×*-un-lft-identity_binary64_2069
27×add-sqr-sqrt_binary64_2091 add-cube-cbrt_binary64_2104
12×unpow-prod-down_binary64_2148 cube-prod_binary64_2097 associate-/r*_binary64_2013
add-exp-log_binary64_2107
add-log-exp_binary64_2108 cube-mult_binary64_2099 add-cbrt-cube_binary64_2105 sqr-pow_binary64_2041 unpow3_binary64_2135
associate-/l*_binary64_2014 div-exp_binary64_2120
pow1_binary64_2130 distribute-lft-out_binary64_2020
frac-2neg_binary64_2080 div-inv_binary64_2066 clear-num_binary64_2068 flip-+_binary64_2043 pow-to-exp_binary64_2138 +-commutative_binary64_1999 cbrt-undiv_binary64_2103 frac-add_binary64_2077 pow-exp_binary64_2137 flip3-+_binary64_2072 sum-log_binary64_2160
Counts
2 → 79
Calls

4 calls:

28.0ms
(+.f64 (/.f64 1/2 x) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))
6.0ms
(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))
0.0ms
(+.f64 (/.f64 1/2 x) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))
0.0ms
(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

series100.0ms (1%)

Counts
2 → 9
Calls

2 calls:

68.0ms
(+.f64 (/.f64 1/2 x) (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)))
32.0ms
(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))
Compiler

Compiled 143 to 131 computations (8.4% saved)

simplify58.0ms (0.6%)

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049771153
149771153

prune76.0ms (0.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New88088
Fresh000
Picked011
Done011
Total88290
Error
0b
Counts
90 → 2
Compiler

Compiled 1224 to 915 computations (25.2% saved)

simplify39.0ms (0.4%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
02993002
12993002

regimes185.0ms (1.9%)

Accuracy

Total 0.0b remaining (96%)

Threshold costs 0.0b (96%)

Compiler

Compiled 2004 to 1510 computations (24.7% saved)

bsearch132.0ms (1.4%)

Steps
ItersRangePoint
8
111.8049958743126
1017956.7090716362
6118.7669097207545
11
-935129.885768049
-4.3455896139349407e-14
-129473.91729072884
Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
088144
188144

end0.0ms (0%)

sample6.1s (63%)

Algorithm
intervals
Results
1.1s8000×body128valid
Compiler

Compiled 6374 to 4726 computations (25.9% saved)

Pareto

-0.031482401391182836

Profiling

Loading profile data...