Details

Time bar (total: 10.2s)

analyze522.0ms (5.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
6.2%93.6%0.2%8
25%74.9%0.2%9
28.1%71.7%0.2%10
29.6%70.2%0.2%11
53%46.8%0.2%12
71.3%28.5%0.2%13
71.7%28.1%0.2%14
Compiler

Compiled 16 to 12 computations (25% saved)

sample25.0ms (0.2%)

Algorithm
intervals
Results
10.0ms256×body128valid
1.0ms20×body128invalid
Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify92.0ms (0.9%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01830
11830

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
27.3b
Counts
2 → 1
Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.1%)

Local error

Found 6 expressions with local error:

26.7b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
0.3b
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.0b
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
0.0b
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
0.3b
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
26.7b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64_1464 add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
times-frac_binary64_1448
add-log-exp_binary64_1481
add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
flip3-+_binary64_1445 flip-+_binary64_1416
associate-/r*_binary64_1386 associate-/l*_binary64_1387 pow1_binary64_1503
sum-log_binary64_1533 associate-/l/_binary64_1389 associate-/r/_binary64_1388 +-commutative_binary64_1372
cbrt-undiv_binary64_1476 div-inv_binary64_1439 clear-num_binary64_1441 frac-2neg_binary64_1453 div-exp_binary64_1493
Counts
3 → 53
Calls

6 calls:

9.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
4.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
4.0ms
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
0.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

series510.0ms (5%)

Counts
3 → 60
Calls

3 calls:

291.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
135.0ms
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
84.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
Compiler

Compiled 1290 to 1074 computations (16.7% saved)

simplify102.0ms (1%)

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
050512576

prune192.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1058113
Fresh000
Picked101
Done000
Total1068114
Error
5.0b
Counts
114 → 8
Compiler

Compiled 2231 to 818 computations (63.3% saved)

localize18.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.1b
(/.f64 (/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))))
0.0b
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
0.3b
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
16.5b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
30.2b
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.2b
(sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

rewrite41.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity_binary64_1442
28×sqrt-prod_binary64_1458
25×add-sqr-sqrt_binary64_1464
24×times-frac_binary64_1448
23×add-cube-cbrt_binary64_1477
10×distribute-lft-out_binary64_1393 unpow-prod-down_binary64_1521
associate-/r*_binary64_1386
add-cbrt-cube_binary64_1478 sqrt-div_binary64_1459 add-log-exp_binary64_1481 add-exp-log_binary64_1480 pow1_binary64_1503
flip3-+_binary64_1445 flip-+_binary64_1416
associate-/l*_binary64_1387
sqrt-pow1_binary64_1460 rem-sqrt-square_binary64_1455 associate-/l/_binary64_1389 associate-/r/_binary64_1388 pow1/2_binary64_1522
cbrt-undiv_binary64_1476 sum-log_binary64_1533 div-inv_binary64_1439 clear-num_binary64_1441 +-commutative_binary64_1372 frac-2neg_binary64_1453 div-exp_binary64_1493
Counts
4 → 94
Calls

8 calls:

15.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
4.0ms
(sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
0.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))

series815.0ms (8%)

Counts
4 → 92
Calls

4 calls:

401.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
155.0ms
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
133.0ms
(sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
126.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
Compiler

Compiled 3500 to 2730 computations (22% saved)

simplify124.0ms (1.2%)

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
049604771
149604771

prune211.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1860186
Fresh077
Picked011
Done000
Total1868194
Error
5.0b
Counts
194 → 8
Compiler

Compiled 5619 to 2278 computations (59.5% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

26.2b
(*.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
0.7b
(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
0.3b
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.0b
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.3b
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.7b
(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.2b
(*.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

rewrite52.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity_binary64_1442
32×times-frac_binary64_1448
31×add-sqr-sqrt_binary64_1464
24×add-cube-cbrt_binary64_1477
21×associate-*r*_binary64_1382
17×add-exp-log_binary64_1480
16×distribute-lft-out_binary64_1393 unpow-prod-down_binary64_1521
11×add-cbrt-cube_binary64_1478
add-log-exp_binary64_1481
pow1_binary64_1503
flip3-+_binary64_1445 flip-+_binary64_1416
associate-/r*_binary64_1386
associate-/r/_binary64_1388 prod-exp_binary64_1491 div-exp_binary64_1493
associate-/l*_binary64_1387 associate-*l*_binary64_1383 unswap-sqr_binary64_1410
cbrt-undiv_binary64_1476 cbrt-unprod_binary64_1475 sum-log_binary64_1533 div-inv_binary64_1439 1-exp_binary64_1486 +-commutative_binary64_1372 rec-exp_binary64_1492 frac-times_binary64_1452 associate-*l/_binary64_1385
associate-*r/_binary64_1384 inv-pow_binary64_1527 clear-num_binary64_1441 pow-prod-down_binary64_1513 *-commutative_binary64_1373 pow-flip_binary64_1516 frac-2neg_binary64_1453 un-div-inv_binary64_1440
Counts
4 → 113
Calls

8 calls:

21.0ms
(*.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
10.0ms
(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
4.0ms
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.0ms
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

series585.0ms (5.8%)

Counts
4 → 69
Calls

4 calls:

296.0ms
(*.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
142.0ms
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
87.0ms
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
60.0ms
(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
Compiler

Compiled 1689 to 1506 computations (10.8% saved)

simplify89.0ms (0.9%)

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049323708
149323708

prune173.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1820182
Fresh066
Picked011
Done011
Total1828190
Error
5.0b
Counts
190 → 8
Compiler

Compiled 3765 to 1995 computations (47% saved)

localize19.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.0b
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
22.9b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
31.2b
(cbrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
31.2b
(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.2b
(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite56.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
18×cbrt-div_binary64_1474
17×*-un-lft-identity_binary64_1442
13×cbrt-prod_binary64_1473
10×flip3-+_binary64_1445 flip-+_binary64_1416
add-exp-log_binary64_1480 add-sqr-sqrt_binary64_1464 add-cube-cbrt_binary64_1477
associate-/r/_binary64_1388
add-cbrt-cube_binary64_1478
add-log-exp_binary64_1481 distribute-lft-out_binary64_1393 frac-times_binary64_1452 pow1_binary64_1503 unpow-prod-down_binary64_1521
times-frac_binary64_1448 associate-/l*_binary64_1387 pow1/3_binary64_1524
associate-*r/_binary64_1384 cbrt-undiv_binary64_1476 associate-/l/_binary64_1389 associate-*l/_binary64_1385 div-exp_binary64_1493
associate-/r*_binary64_1386 cbrt-unprod_binary64_1475 div-inv_binary64_1439 clear-num_binary64_1441 frac-2neg_binary64_1453 prod-exp_binary64_1491
Counts
4 → 74
Calls

8 calls:

27.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
7.0ms
(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
7.0ms
(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms
(cbrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
0.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))

series1.5s (14.5%)

Counts
4 → 60
Calls

4 calls:

958.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
176.0ms
(cbrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
171.0ms
(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
169.0ms
(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
Compiler

Compiled 3642 to 2982 computations (18.1% saved)

simplify125.0ms (1.2%)

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 0 (87.0ms)

IterNodesCost
049603482
149603482

prune214.0ms (2.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1340134
Fresh055
Picked011
Done022
Total1348142
Error
5.0b
Counts
142 → 8
Compiler

Compiled 4967 to 2542 computations (48.8% saved)

simplify25.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
02501683
12501683

regimes758.0ms (7.5%)

Compiler

Compiled 4526 to 3297 computations (27.2% saved)

bsearch86.0ms (0.8%)

Steps
ItersRangePoint
9
5.261012177257102e+79
9.232655022452831e+86
1.315316451044619e+86
6
1.4455124447971334e-123
7.993289479926725e-123
2.1472644582174967e-123
10
-1.5447351947110331e-100
-1.2451099552022908e-113
-8.849808015292707e-110
8
-4.362551450141799e+80
-1.5989624956840602e+77
-2.7839182926984815e+79
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes495.0ms (4.9%)

Compiler

Compiled 2326 to 1852 computations (20.4% saved)

bsearch78.0ms (0.8%)

Steps
ItersRangePoint
9
5.261012177257102e+79
9.232655022452831e+86
4.534169458994563e+85
6
1.4455124447971334e-123
7.993289479926725e-123
4.231028026572649e-123
10
-1.5447351947110331e-100
-1.2451099552022908e-113
-3.697868456727824e-105
8
-4.362551450141799e+80
-1.5989624956840602e+77
-3.88489195189713e+80
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes311.0ms (3.1%)

Compiler

Compiled 891 to 877 computations (1.6% saved)

bsearch78.0ms (0.8%)

Steps
ItersRangePoint
9
5.261012177257102e+79
9.232655022452831e+86
7.627044215435255e+80
6
1.4455124447971334e-123
7.993289479926725e-123
2.7738332462896228e-123
10
-1.5447351947110331e-100
-1.2451099552022908e-113
-2.5452377900992097e-111
8
-4.362551450141799e+80
-1.5989624956840602e+77
-3.067174421205907e+78
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes211.0ms (2.1%)

Compiler

Compiled 426 to 472 computations (-10.8% saved)

bsearch71.0ms (0.7%)

Steps
ItersRangePoint
4
1.0809080973822217e+148
1.872942754955432e+148
1.285252112405183e+148
6
1.4455124447971334e-123
7.993289479926725e-123
1.577656469061019e-123
10
-1.5447351947110331e-100
-1.2451099552022908e-113
-1.2072253979978834e-112
8
-4.362551450141799e+80
-1.5989624956840602e+77
-1.4298120870909682e+80
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes192.0ms (1.9%)

Compiler

Compiled 371 to 422 computations (-13.7% saved)

bsearch60.0ms (0.6%)

Steps
ItersRangePoint
4
1.0809080973822217e+148
1.872942754955432e+148
1.5945629769053138e+148
6
1.4455124447971334e-123
7.993289479926725e-123
4.3449496244039453e-123
9
-4.842386570855476e-123
-1.6010944888570607e-131
-4.376913782191672e-128
8
-4.362551450141799e+80
-1.5989624956840602e+77
-8.061965778995371e+78
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes188.0ms (1.8%)

Compiler

Compiled 132 to 204 computations (-54.5% saved)

bsearch95.0ms (0.9%)

Steps
ItersRangePoint
9
5.261012177257102e+79
9.232655022452831e+86
6.528621872342922e+83
9
4.782406745779112e+39
6.3437690306833865e+44
1.4572556395906934e+44
9
3.721174892280916e-55
1.4967404820226354e-47
1.0125679456766562e-47
8
-1.2451099552022908e-113
-1.0941812263563016e-116
-5.953797694454756e-116
10
-3.33646812185011e+40
-6.261549615938781e+30
-5.4255857942412725e+39
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes179.0ms (1.8%)

Compiler

Compiled 88 to 168 computations (-90.9% saved)

bsearch58.0ms (0.6%)

Steps
ItersRangePoint
9
5.261012177257102e+79
9.232655022452831e+86
3.4503959034734146e+81
4
-1.4759290785408983e-74
-8.624414968021159e-75
-1.4560731490103253e-74
9
-4000405.996115119
-1.6834101773030716
-2271.1008849571535
7
-2.5571681320258447e+43
-1.1605460571496514e+42
-1.1727455119206626e+42
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes54.0ms (0.5%)

Compiler

Compiled 32 to 112 computations (-250% saved)

bsearch14.0ms (0.1%)

Steps
ItersRangePoint
6
-1.6934845283067424e+131
-1.5117820023391907e+130
-1.4722939306885992e+131
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes32.0ms (0.3%)

Accuracy

Total 9.5b remaining (66.1%)

Threshold costs 0b (0%)

Compiler

Compiled 20 to 92 computations (-360% saved)

bsearch15.0ms (0.1%)

Compiler

Compiled 448 to 240 computations (46.4% saved)

simplify12.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0151835
1151835

end0.0ms (0%)

sample1.7s (16.3%)

Algorithm
intervals
Results
338.0ms8000×body128valid
18.0ms443×body128invalid
Compiler

Compiled 1345 to 897 computations (33.3% saved)

Pareto

0.9448859384098013

Profiling

Loading profile data...