Details

Time bar (total: 6.1s)

analyze505.0ms (8.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
18.7%81.1%0.1%7
21.8%78%0.1%8
21.8%78%0.1%9
49.1%50.7%0.1%10
52.7%47.2%0.1%11
52.7%47.2%0.1%12
71.7%28.2%0.1%13
74.1%25.8%0.1%14
Compiler

Compiled 22 to 19 computations (13.6% saved)

sample22.0ms (0.4%)

Algorithm
intervals
Results
13.0ms256×body128valid
Compiler

Compiled 43 to 40 computations (7% saved)

simplify184.0ms (3%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (13.0ms)

IterNodesCost
045331
145331

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 18.9b

Counts
2 → 1
Compiler

Compiled 42 to 36 computations (14.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))
0.1b
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
3.6b
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
18.6b
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite63.0ms (1%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64_6981
13×add-exp-log_binary64_6997 add-cbrt-cube_binary64_6995
12×*-un-lft-identity_binary64_6959
10×add-cube-cbrt_binary64_6994
pow1_binary64_7020
associate-*r*_binary64_6899 associate-*l*_binary64_6900 add-log-exp_binary64_6998
flip3-+_binary64_6962 flip-+_binary64_6933
associate-*r/_binary64_6901
cbrt-unprod_binary64_6992 associate-/r*_binary64_6903 prod-exp_binary64_7008 times-frac_binary64_6965
pow-prod-down_binary64_7030 associate-/l/_binary64_6906 *-commutative_binary64_6890 unswap-sqr_binary64_6927 associate-*l/_binary64_6902 associate-/r/_binary64_6905 div-exp_binary64_7010 cbrt-undiv_binary64_6993
sum-log_binary64_7050 distribute-rgt-in_binary64_6909 frac-2neg_binary64_6970 div-inv_binary64_6956 distribute-lft-out_binary64_6910 associate-/l*_binary64_6904 clear-num_binary64_6958 +-commutative_binary64_6889 distribute-lft-in_binary64_6908
Counts
4 → 79
Calls

4 calls:

22.0ms
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
12.0ms
(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))
12.0ms
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
8.0ms
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)

series820.0ms (13.5%)

Counts
4 → 12
Calls

4 calls:

465.0ms
(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))
200.0ms
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
80.0ms
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
74.0ms
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)

simplify75.0ms (1.2%)

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
049392199
149392199

prune253.0ms (4.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New87491
Fresh000
Picked101
Done000
Total88492

Merged error: 0.0b

Counts
92 → 4
Compiler

Compiled 4755 to 3712 computations (21.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 x (*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
0.1b
(*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.1b
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
15.4b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite60.0ms (1%)

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64_6981
22×*-un-lft-identity_binary64_6959 add-cube-cbrt_binary64_6994
19×times-frac_binary64_6965
18×associate-*r*_binary64_6899
13×add-exp-log_binary64_6997 add-cbrt-cube_binary64_6995
pow1_binary64_7020
associate-*l*_binary64_6900 add-log-exp_binary64_6998
flip3-+_binary64_6962 flip-+_binary64_6933
associate-/r/_binary64_6905
associate-*r/_binary64_6901 unswap-sqr_binary64_6927 associate-/l*_binary64_6904 cbrt-unprod_binary64_6992 associate-/r*_binary64_6903 prod-exp_binary64_7008
pow-prod-down_binary64_7030 associate-/l/_binary64_6906 *-commutative_binary64_6890 div-inv_binary64_6956 div-exp_binary64_7010 cbrt-undiv_binary64_6993
sum-log_binary64_7050 distribute-rgt-in_binary64_6909 frac-2neg_binary64_6970 clear-num_binary64_6958 +-commutative_binary64_6889 distribute-lft-in_binary64_6908
Counts
4 → 98
Calls

4 calls:

21.0ms
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
17.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
8.0ms
(*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
4.0ms
(+.f64 x (*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))

series788.0ms (13%)

Counts
4 → 12
Calls

4 calls:

453.0ms
(+.f64 x (*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
195.0ms
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
90.0ms
(*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
49.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify64.0ms (1%)

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
050103185

prune205.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1091110
Fresh033
Picked011
Done000
Total1095114

Merged error: 0.0b

Counts
114 → 5
Compiler

Compiled 4139 to 3140 computations (24.1% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
15.4b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
15.4b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
15.4b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite92.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
36×times-frac_binary64_6965
35×*-un-lft-identity_binary64_6959 add-cube-cbrt_binary64_6994 add-sqr-sqrt_binary64_6981
15×cbrt-prod_binary64_6990
10×add-exp-log_binary64_6997 add-cbrt-cube_binary64_6995
associate-/l*_binary64_6904 associate-/r*_binary64_6903
associate-/r/_binary64_6905
flip3-+_binary64_6962 flip-+_binary64_6933
associate-/l/_binary64_6906
div-inv_binary64_6956 pow1_binary64_7020 add-log-exp_binary64_6998
frac-2neg_binary64_6970 clear-num_binary64_6958 div-exp_binary64_7010 cbrt-undiv_binary64_6993
pow1/3_binary64_7041 cbrt-div_binary64_6991
Counts
4 → 117
Calls

4 calls:

20.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
18.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
17.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
15.0ms
(cbrt.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

series191.0ms (3.2%)

Counts
4 → 12
Calls

4 calls:

72.0ms
(cbrt.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
42.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
39.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
38.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify104.0ms (1.7%)

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
048984743
148984743

prune627.0ms (10.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1290129
Fresh033
Picked011
Done011
Total1295134

Merged error: 0.0b

Counts
134 → 5
Compiler

Compiled 9396 to 7291 computations (22.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.6b
(*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
14.6b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
14.7b
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
14.7b
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite104.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt_binary64_6981
66×times-frac_binary64_6965
47×*-un-lft-identity_binary64_6959 add-cube-cbrt_binary64_6994
42×sqrt-prod_binary64_6975
24×associate-*r*_binary64_6899 associate-*l*_binary64_6900
18×add-exp-log_binary64_6997 add-cbrt-cube_binary64_6995
10×sqrt-div_binary64_6976
unswap-sqr_binary64_6927
pow1_binary64_7020
flip3-+_binary64_6962 flip-+_binary64_6933 associate-/r*_binary64_6903 associate-/r/_binary64_6905
div-exp_binary64_7010 cbrt-undiv_binary64_6993
cbrt-unprod_binary64_6992 add-log-exp_binary64_6998 prod-exp_binary64_7008
div-inv_binary64_6956 associate-/l*_binary64_6904
pow1/2_binary64_7039 associate-/l/_binary64_6906 sqrt-pow1_binary64_6977 rem-sqrt-square_binary64_6972
associate-*r/_binary64_6901 pow-prod-down_binary64_7030 frac-2neg_binary64_6970 frac-times_binary64_6969 *-commutative_binary64_6890 associate-*l/_binary64_6902 clear-num_binary64_6958
Counts
4 → 150
Calls

4 calls:

47.0ms
(*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
18.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
8.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
7.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

series317.0ms (5.2%)

Counts
4 → 12
Calls

4 calls:

188.0ms
(*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
64.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
33.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
32.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify100.0ms (1.6%)

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
052336204

prune421.0ms (6.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1620162
Fresh022
Picked011
Done022
Total1625167

Merged error: 0.0b

Counts
167 → 5
Compiler

Compiled 7104 to 5395 computations (24.1% saved)

regimes115.0ms (1.9%)

Compiler

Compiled 447 to 390 computations (12.8% saved)

bsearch46.0ms (0.8%)

Steps
ItersRangePoint
8
522.678295489821
870482.2626791305
859587.4586008149
8
-62220938.70655694
-3882.644648931999
-61306154.06441152
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04861
14861

end0.0ms (0%)

sample838.0ms (13.8%)

Algorithm
intervals
Results
429.0ms8000×body128valid
Compiler

Compiled 275 to 225 computations (18.2% saved)

Profiling

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