Details

Time bar (total: 5.0s)

analyze501.0ms (10.1%)

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)

sample21.0ms (0.4%)

Algorithm
intervals
Results
13.0ms256×body128valid
Compiler

Compiled 43 to 40 computations (7% saved)

simplify177.0ms (3.5%)

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

Merged error: 20.2b

Counts
2 → 1
Compiler

Compiled 42 to 36 computations (14.3% saved)

localize14.0ms (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)
5.4b
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
19.5b
(/.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%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64_10545
15×add-exp-log_binary64_10559 add-cbrt-cube_binary64_10557
14×*-un-lft-identity_binary64_10524
12×add-cube-cbrt_binary64_10556
10×pow1_binary64_10582 associate-*l*_binary64_10467
associate-*r*_binary64_10466
flip3-+_binary64_10527 flip-+_binary64_10498
prod-exp_binary64_10570 cbrt-unprod_binary64_10554 associate-*r/_binary64_10468 add-log-exp_binary64_10560 associate-*l/_binary64_10469
pow-prod-down_binary64_10592 *-commutative_binary64_10457 times-frac_binary64_10530 unswap-sqr_binary64_10492 associate-/r*_binary64_10470
div-exp_binary64_10572 associate-/r/_binary64_10472 associate-/l/_binary64_10473 cbrt-undiv_binary64_10555
associate-/l*_binary64_10471 frac-2neg_binary64_10535 distribute-lft-out_binary64_10477 clear-num_binary64_10523 distribute-lft-in_binary64_10475 div-inv_binary64_10521 distribute-rgt-in_binary64_10476
Counts
4 → 88
Calls

4 calls:

17.0ms
(/.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 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
8.0ms
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
6.0ms
(*.f64 (+.f64 z 1692356830115869/281474976710656) z)

series424.0ms (8.5%)

Counts
4 → 12
Calls

4 calls:

198.0ms
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
82.0ms
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
80.0ms
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
64.0ms
(*.f64 (+.f64 z 1692356830115869/281474976710656) z)

simplify57.0ms (1.1%)

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
050121847

prune159.0ms (3.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New964100
Fresh000
Picked101
Done000
Total974101

Merged error: 0.0b

Counts
101 → 4
Compiler

Compiled 2805 to 2061 computations (26.5% saved)

localize14.0ms (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)))
16.8b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite60.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64_10545
26×*-un-lft-identity_binary64_10524
24×add-cube-cbrt_binary64_10556
22×associate-*r*_binary64_10466
19×times-frac_binary64_10530
15×add-exp-log_binary64_10559 add-cbrt-cube_binary64_10557
10×pow1_binary64_10582
associate-*l*_binary64_10467
associate-*r/_binary64_10468 flip3-+_binary64_10527 flip-+_binary64_10498
prod-exp_binary64_10570 cbrt-unprod_binary64_10554 associate-/r/_binary64_10472 unswap-sqr_binary64_10492 add-log-exp_binary64_10560
pow-prod-down_binary64_10592 *-commutative_binary64_10457 associate-/l*_binary64_10471 associate-/r*_binary64_10470
div-exp_binary64_10572 associate-/l/_binary64_10473 distribute-lft-in_binary64_10475 cbrt-undiv_binary64_10555 div-inv_binary64_10521 distribute-rgt-in_binary64_10476
frac-2neg_binary64_10535 distribute-lft-out_binary64_10477 clear-num_binary64_10523
Counts
4 → 110
Calls

4 calls:

18.0ms
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
16.0ms
(/.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))
7.0ms
(*.f64 z (+.f64 z 1692356830115869/281474976710656))

series360.0ms (7.2%)

Counts
4 → 12
Calls

4 calls:

185.0ms
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
73.0ms
(*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
55.0ms
(*.f64 z (+.f64 z 1692356830115869/281474976710656))
47.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify63.0ms (1.3%)

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
051802874

prune188.0ms (3.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1211122
Fresh033
Picked101
Done000
Total1224126

Merged error: 0b

Counts
126 → 4
Compiler

Compiled 3716 to 2750 computations (26% saved)

localize21.0ms (0.4%)

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))))
16.1b
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
16.1b
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
16.2b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

rewrite97.0ms (2%)

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt_binary64_10545
66×times-frac_binary64_10530
47×*-un-lft-identity_binary64_10524 add-cube-cbrt_binary64_10556
42×sqrt-prod_binary64_10539
24×associate-*l*_binary64_10467 associate-*r*_binary64_10466
18×add-exp-log_binary64_10559 add-cbrt-cube_binary64_10557
10×sqrt-div_binary64_10540
unswap-sqr_binary64_10492
pow1_binary64_10582
associate-/r/_binary64_10472 flip3-+_binary64_10527 associate-/r*_binary64_10470 flip-+_binary64_10498
div-exp_binary64_10572 cbrt-undiv_binary64_10555
prod-exp_binary64_10570 cbrt-unprod_binary64_10554 add-log-exp_binary64_10560
associate-/l*_binary64_10471 div-inv_binary64_10521
rem-sqrt-square_binary64_10537 sqrt-pow1_binary64_10541 pow1/2_binary64_10601 associate-/l/_binary64_10473
pow-prod-down_binary64_10592 *-commutative_binary64_10457 frac-2neg_binary64_10535 associate-*r/_binary64_10468 clear-num_binary64_10523 frac-times_binary64_10534 associate-*l/_binary64_10469
Counts
4 → 150
Calls

4 calls:

38.0ms
(*.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))))
17.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
7.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
7.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

series318.0ms (6.4%)

Counts
4 → 12
Calls

4 calls:

185.0ms
(*.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))))
65.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
36.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
31.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify99.0ms (2%)

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
051286204

prune407.0ms (8.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1620162
Fresh033
Picked011
Done000
Total1624166

Merged error: 0b

Counts
166 → 4
Compiler

Compiled 6983 to 5294 computations (24.2% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 y (cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) 3)))
0.5b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) 3))
0.5b
(pow.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) 3)
16.8b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite108.0ms (2.2%)

Algorithm
rewrite-expression-head
Rules
78×cbrt-prod_binary64_10552
74×add-sqr-sqrt_binary64_10545
65×times-frac_binary64_10530
59×*-un-lft-identity_binary64_10524 add-cube-cbrt_binary64_10556
47×unpow-prod-down_binary64_10600 cube-prod_binary64_10549
39×associate-*r*_binary64_10466
14×associate-/r/_binary64_10472
11×add-exp-log_binary64_10559
10×add-cbrt-cube_binary64_10557
flip3-+_binary64_10527 flip-+_binary64_10498
pow1_binary64_10582 unswap-sqr_binary64_10492 div-inv_binary64_10521
add-log-exp_binary64_10560 sqr-pow_binary64_10496
cube-div_binary64_10550 pow-unpow_binary64_10598 unpow3_binary64_10587 associate-/l*_binary64_10471 associate-*l*_binary64_10467 associate-/r*_binary64_10470 cube-mult_binary64_10551
rem-cube-cbrt_binary64_10546 div-exp_binary64_10572 cbrt-div_binary64_10553 pow-exp_binary64_10589 associate-/l/_binary64_10473 cbrt-undiv_binary64_10555
pow-pow_binary64_10593 pow-prod-down_binary64_10592 prod-exp_binary64_10570 *-commutative_binary64_10457 pow-to-exp_binary64_10590 cbrt-unprod_binary64_10554 frac-2neg_binary64_10535 pow1/3_binary64_10603 associate-*r/_binary64_10468 clear-num_binary64_10523 rem-cbrt-cube_binary64_10547
Counts
4 → 188
Calls

4 calls:

26.0ms
(*.f64 y (cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) 3)))
16.0ms
(pow.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) 3)
16.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
16.0ms
(cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) 3))

series310.0ms (6.2%)

Counts
4 → 12
Calls

4 calls:

184.0ms
(*.f64 y (cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) 3)))
43.0ms
(pow.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) 3)
43.0ms
(cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) 3))
38.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify115.0ms (2.3%)

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049487158
149487158

prune434.0ms (8.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2000200
Fresh022
Picked011
Done011
Total2004204

Merged error: 0b

Counts
204 → 4
Compiler

Compiled 7127 to 5442 computations (23.6% saved)

regimes100.0ms (2%)

Compiler

Compiled 279 to 252 computations (9.7% saved)

bsearch62.0ms (1.2%)

Steps
ItersRangePoint
10
2.7826861966151592e-11
3568.250745215279
3521.4206826746104
10
-5.540292547950922e+29
-5.655785173204798e+17
-3.4752457487355863e+18
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07172
17172

end0.0ms (0%)

sample801.0ms (16.1%)

Algorithm
intervals
Results
418.0ms8000×body128valid
Compiler

Compiled 226 to 185 computations (18.1% saved)

Profiling

Loading profile data...