Details

Time bar (total: 4.6s)

analyze480.0ms (10.4%)

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)

sample20.0ms (0.4%)

Algorithm
intervals
Results
12.0ms256×body128valid
Compiler

Compiled 43 to 40 computations (7% saved)

simplify109.0ms (2.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (13.0ms)

IterNodesCost
045331
145331

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
20.9b
Counts
2 → 1
Compiler

Compiled 42 to 36 computations (14.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
0.1b
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
5.5b
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
20.1b
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite51.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64_9989
15×add-cbrt-cube_binary64_10003 add-exp-log_binary64_10005
14×*-un-lft-identity_binary64_9967
12×add-cube-cbrt_binary64_10002
10×associate-*l*_binary64_9908 pow1_binary64_10028
associate-*r*_binary64_9907
flip3-+_binary64_9970 flip-+_binary64_9941
prod-exp_binary64_10016 cbrt-unprod_binary64_10000 associate-*l/_binary64_9910 add-log-exp_binary64_10006 associate-*r/_binary64_9909
times-frac_binary64_9973 pow-prod-down_binary64_10038 unswap-sqr_binary64_9935 associate-/r*_binary64_9911 *-commutative_binary64_9898
div-exp_binary64_10018 cbrt-undiv_binary64_10001 associate-/l/_binary64_9914 associate-/r/_binary64_9913
distribute-lft-out_binary64_9918 distribute-lft-in_binary64_9916 associate-/l*_binary64_9912 distribute-rgt-in_binary64_9917 div-inv_binary64_9964 frac-2neg_binary64_9978 clear-num_binary64_9966
Counts
4 → 88
Calls

4 calls:

16.0ms
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
11.0ms
(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
10.0ms
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
7.0ms
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)

series205.0ms (4.4%)

Counts
4 → 12
Calls

4 calls:

99.0ms
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
40.0ms
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
38.0ms
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
27.0ms
(*.f64 (+.f64 z 1692356830115869/281474976710656) z)

simplify89.0ms (1.9%)

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
050211847

prune152.0ms (3.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New964100
Fresh000
Picked101
Done000
Total974101
Error
0b
Counts
101 → 4
Compiler

Compiled 2825 to 2077 computations (26.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 z (+.f64 z 1692356830115869/281474976710656))
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)))
16.1b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite54.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64_9989
26×*-un-lft-identity_binary64_9967
24×add-cube-cbrt_binary64_10002
22×associate-*r*_binary64_9907
19×times-frac_binary64_9973
15×add-cbrt-cube_binary64_10003 add-exp-log_binary64_10005
10×pow1_binary64_10028
associate-*l*_binary64_9908
flip3-+_binary64_9970 flip-+_binary64_9941 associate-*r/_binary64_9909
prod-exp_binary64_10016 cbrt-unprod_binary64_10000 add-log-exp_binary64_10006 unswap-sqr_binary64_9935 associate-/r/_binary64_9913
associate-/l*_binary64_9912 pow-prod-down_binary64_10038 associate-/r*_binary64_9911 *-commutative_binary64_9898
div-exp_binary64_10018 cbrt-undiv_binary64_10001 associate-/l/_binary64_9914 distribute-lft-in_binary64_9916 distribute-rgt-in_binary64_9917 div-inv_binary64_9964
distribute-lft-out_binary64_9918 frac-2neg_binary64_9978 clear-num_binary64_9966
Counts
4 → 110
Calls

4 calls:

17.0ms
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
14.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
7.0ms
(*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
6.0ms
(*.f64 z (+.f64 z 1692356830115869/281474976710656))

series183.0ms (3.9%)

Counts
4 → 12
Calls

4 calls:

89.0ms
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
37.0ms
(*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
28.0ms
(*.f64 z (+.f64 z 1692356830115869/281474976710656))
28.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify86.0ms (1.9%)

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
048992874
148992874

prune183.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1220122
Fresh033
Picked011
Done000
Total1224126
Error
0b
Counts
126 → 4
Compiler

Compiled 3712 to 2746 computations (26% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.6b
(*.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))))
15.5b
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
15.5b
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
15.5b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

rewrite85.0ms (1.8%)

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt_binary64_9989
66×times-frac_binary64_9973
47×add-cube-cbrt_binary64_10002 *-un-lft-identity_binary64_9967
42×sqrt-prod_binary64_9983
24×associate-*l*_binary64_9908 associate-*r*_binary64_9907
18×add-cbrt-cube_binary64_10003 add-exp-log_binary64_10005
10×sqrt-div_binary64_9984
unswap-sqr_binary64_9935
pow1_binary64_10028
flip3-+_binary64_9970 flip-+_binary64_9941 associate-/r*_binary64_9911 associate-/r/_binary64_9913
div-exp_binary64_10018 cbrt-undiv_binary64_10001
prod-exp_binary64_10016 cbrt-unprod_binary64_10000 add-log-exp_binary64_10006
associate-/l*_binary64_9912 div-inv_binary64_9964
associate-/l/_binary64_9914 pow1/2_binary64_10047 sqrt-pow1_binary64_9985 rem-sqrt-square_binary64_9980
frac-times_binary64_9977 associate-*l/_binary64_9910 pow-prod-down_binary64_10038 associate-*r/_binary64_9909 frac-2neg_binary64_9978 clear-num_binary64_9966 *-commutative_binary64_9898
Counts
4 → 150
Calls

4 calls:

35.0ms
(*.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))))
16.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
9.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
6.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

series159.0ms (3.4%)

Counts
4 → 12
Calls

4 calls:

88.0ms
(*.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))))
33.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
21.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
17.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify97.0ms (2.1%)

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
053236204

prune395.0ms (8.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1620162
Fresh022
Picked011
Done011
Total1624166
Error
0b
Counts
166 → 4
Compiler

Compiled 6979 to 5289 computations (24.2% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
0.2b
(*.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z))
1.7b
(*.f64 y (-.f64 (*.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)) (*.f64 5029535718965825/18014398509481984 5029535718965825/18014398509481984)))
24.8b
(/.f64 (*.f64 y (-.f64 (*.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)) (*.f64 5029535718965825/18014398509481984 5029535718965825/18014398509481984))) (*.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (-.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))

rewrite90.0ms (1.9%)

Algorithm
rewrite-expression-head
Rules
47×pow1_binary64_10028
32×add-cbrt-cube_binary64_10003 add-exp-log_binary64_10005
19×pow-prod-down_binary64_10038
18×associate-*l/_binary64_9910
14×prod-exp_binary64_10016 cbrt-unprod_binary64_10000
12×add-sqr-sqrt_binary64_9989
10×flip3-+_binary64_9970 flip-+_binary64_9941
frac-times_binary64_9977 associate-*r*_binary64_9907 add-cube-cbrt_binary64_10002 *-un-lft-identity_binary64_9967 associate-*r/_binary64_9909 associate-/r/_binary64_9913
associate-*l*_binary64_9908
flip--_binary64_9942 flip3--_binary64_9971
div-exp_binary64_10018 cbrt-undiv_binary64_10001 add-log-exp_binary64_10006 pow-sqr_binary64_9940 pow-prod-up_binary64_10037
*-commutative_binary64_9898
associate-/l/_binary64_9914 sub-neg_binary64_9960 distribute-lft-in_binary64_9916 distribute-rgt-in_binary64_9917 unswap-sqr_binary64_9935 pow-plus_binary64_10030 cancel-sign-sub-inv_binary64_9933
times-frac_binary64_9973 swap-sqr_binary64_9934 difference-of-squares_binary64_9936 associate-/l*_binary64_9912 pow2_binary64_10048 div-inv_binary64_9964 associate-/r*_binary64_9911 frac-2neg_binary64_9978 clear-num_binary64_9966
Counts
4 → 118
Calls

4 calls:

31.0ms
(/.f64 (*.f64 y (-.f64 (*.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)) (*.f64 5029535718965825/18014398509481984 5029535718965825/18014398509481984))) (*.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (-.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
17.0ms
(*.f64 y (-.f64 (*.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)) (*.f64 5029535718965825/18014398509481984 5029535718965825/18014398509481984)))
14.0ms
(*.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z))
7.0ms
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)

series321.0ms (6.9%)

Counts
4 → 12
Calls

4 calls:

200.0ms
(/.f64 (*.f64 y (-.f64 (*.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)) (*.f64 5029535718965825/18014398509481984 5029535718965825/18014398509481984))) (*.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (-.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
70.0ms
(*.f64 y (-.f64 (*.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)) (*.f64 5029535718965825/18014398509481984 5029535718965825/18014398509481984)))
35.0ms
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
16.0ms
(*.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z))

simplify86.0ms (1.9%)

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
054743604

prune322.0ms (7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1300130
Fresh011
Picked011
Done022
Total1304134
Error
0b
Counts
134 → 4
Compiler

Compiled 5981 to 4547 computations (24% saved)

regimes311.0ms (6.7%)

Accuracy

Total 0.1b remaining (94.5%)

Threshold costs 0.1b (94.5%)

Compiler

Compiled 2411 to 2033 computations (15.7% saved)

bsearch47.0ms (1%)

Steps
ItersRangePoint
10
0.19282898733107162
265655772685.93762
658686.8388840592
8
-7.42288613694871e+30
-1.5270253286781443e+28
-2.6681944807970624e+30
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06867
16867

end0.0ms (0%)

sample1.0s (22.5%)

Algorithm
intervals
Results
408.0ms8000×body128valid
Compiler

Compiled 597 to 493 computations (17.4% saved)

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