Details

Time bar (total: 20.7s)

analyze139.0ms (0.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14
Compiler

Compiled 39 to 27 computations (30.8% saved)

sample54.0ms (0.3%)

Algorithm
intervals
Results
18.0ms209×body128valid
8.0ms256×pre128true
7.0ms16×body512valid
5.0ms18×body1024valid
2.0ms11×body256valid
1.0msbody2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify334.0ms (1.6%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (141.0ms)

IterNodesCost
0489443
1489443

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 21.6b

Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize27.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
1.4b
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
18.0b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite111.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
54×times-frac_binary64_1461
47×*-un-lft-identity_binary64_1455
25×add-sqr-sqrt_binary64_1477 add-cube-cbrt_binary64_1490
17×add-cbrt-cube_binary64_1491 add-exp-log_binary64_1493
14×associate-/r/_binary64_1401
11×distribute-lft-out_binary64_1406 flip-+_binary64_1429 flip3-+_binary64_1458
10×associate-/l*_binary64_1400
associate-/l/_binary64_1402
div-exp_binary64_1506 associate-/r*_binary64_1399 cbrt-undiv_binary64_1489 div-inv_binary64_1452
add-log-exp_binary64_1494
frac-times_binary64_1465
pow1_binary64_1516 flip--_binary64_1430 flip3--_binary64_1459
prod-exp_binary64_1504 associate-*r/_binary64_1397 clear-num_binary64_1454 frac-2neg_binary64_1466 cbrt-unprod_binary64_1488 associate-*l/_binary64_1398
sum-log_binary64_1546 +-commutative_binary64_1385
Counts
3 → 111
Calls

3 calls:

37.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
29.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
29.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.4s (6.8%)

Counts
3 → 9
Calls

3 calls:

693.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
583.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
127.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify102.0ms (0.5%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049355261
149355261

prune997.0ms (4.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1119120
Fresh000
Picked101
Done000
Total1129121

Merged error: 7.0b

Counts
121 → 9
Compiler

Compiled 25112 to 15106 computations (39.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.3b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.3b
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
6.5b
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite345.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
603×times-frac_binary64_1461
484×*-un-lft-identity_binary64_1455
408×add-sqr-sqrt_binary64_1477
260×add-cube-cbrt_binary64_1490
219×sqrt-prod_binary64_1471
153×associate-*r*_binary64_1395
67×distribute-lft-out_binary64_1406
45×distribute-lft-out--_binary64_1407 difference-of-squares_binary64_1424
38×associate-/r/_binary64_1401
34×associate-*l*_binary64_1396
32×add-cbrt-cube_binary64_1491 add-exp-log_binary64_1493
25×associate-/l*_binary64_1400
21×flip-+_binary64_1429 flip3-+_binary64_1458
19×div-inv_binary64_1452
15×unswap-sqr_binary64_1423
14×associate-/r*_binary64_1399
13×div-exp_binary64_1506 cbrt-undiv_binary64_1489
sqrt-div_binary64_1472
prod-exp_binary64_1504 pow1_binary64_1516 add-log-exp_binary64_1494 cbrt-unprod_binary64_1488
associate-/l/_binary64_1402
clear-num_binary64_1454 frac-2neg_binary64_1466 div-sub_binary64_1460
associate-*r/_binary64_1397 frac-times_binary64_1465 *-commutative_binary64_1386 sum-log_binary64_1546 +-commutative_binary64_1385 associate-*l/_binary64_1398 pow-prod-down_binary64_1526
Counts
4 → 485
Calls

4 calls:

142.0ms
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
49.0ms
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
26.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
15.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

series1.9s (9.4%)

Counts
4 → 12
Calls

4 calls:

692.0ms
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
597.0ms
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
373.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
282.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify241.0ms (1.2%)

Algorithm
egg-herbie
Counts
497 → 497
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
0540027691

prune2.8s (13.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New4934497
Fresh358
Picked011
Done000
Total49610506

Merged error: 7.0b

Counts
506 → 10
Compiler

Compiled 41157 to 24073 computations (41.5% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (+.f64 alpha beta) (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.3b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.4b
(/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
8.4b
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (+.f64 alpha beta) (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))) 1)

rewrite210.0ms (1%)

Algorithm
rewrite-expression-head
Rules
337×times-frac_binary64_1461
301×*-un-lft-identity_binary64_1455
217×add-sqr-sqrt_binary64_1477
187×sqrt-prod_binary64_1471
169×add-cube-cbrt_binary64_1490
42×distribute-lft-out_binary64_1406
28×associate-/l*_binary64_1400
27×associate-/r*_binary64_1399
24×distribute-lft-out--_binary64_1407 difference-of-squares_binary64_1424
22×associate-/r/_binary64_1401
15×add-exp-log_binary64_1493
13×flip-+_binary64_1429 add-cbrt-cube_binary64_1491 flip3-+_binary64_1458
11×div-inv_binary64_1452
10×sqrt-div_binary64_1472
pow1_binary64_1516
div-exp_binary64_1506 add-log-exp_binary64_1494
pow-flip_binary64_1529 cbrt-undiv_binary64_1489
sqrt-pow1_binary64_1473
associate-/l/_binary64_1402 clear-num_binary64_1454 frac-2neg_binary64_1466
pow1/2_binary64_1535 div-sub_binary64_1460
inv-pow_binary64_1540 1-exp_binary64_1499 sum-log_binary64_1546 rec-exp_binary64_1505 +-commutative_binary64_1385
Counts
4 → 339
Calls

4 calls:

69.0ms
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (+.f64 alpha beta) (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))) 1)
26.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
17.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
13.0ms
(/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))

series1.6s (7.9%)

Counts
4 → 12
Calls

4 calls:

681.0ms
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (+.f64 alpha beta) (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))) 1)
349.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
319.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
279.0ms
(/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))

simplify173.0ms (0.8%)

Algorithm
egg-herbie
Counts
351 → 351
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0515717518

prune1.9s (9.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New3483351
Fresh178
Picked011
Done011
Total34912361

Merged error: 7.0b

Counts
361 → 12
Compiler

Compiled 29405 to 17958 computations (38.9% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1))
0.3b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.3b
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
6.5b
(+.f64 1 (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))

rewrite487.0ms (2.4%)

Algorithm
rewrite-expression-head
Rules
825×times-frac_binary64_1461
610×*-un-lft-identity_binary64_1455
564×add-sqr-sqrt_binary64_1477
327×add-cube-cbrt_binary64_1490
264×sqrt-prod_binary64_1471
153×associate-*l*_binary64_1396
106×associate-*r*_binary64_1395
89×distribute-lft-out_binary64_1406
68×add-exp-log_binary64_1493
47×add-cbrt-cube_binary64_1491
45×distribute-lft-out--_binary64_1407 difference-of-squares_binary64_1424
42×associate-/r/_binary64_1401
37×div-exp_binary64_1506
35×unswap-sqr_binary64_1423
25×associate-/l*_binary64_1400
23×flip-+_binary64_1429 flip3-+_binary64_1458
22×cbrt-undiv_binary64_1489 div-inv_binary64_1452
15×prod-exp_binary64_1504
14×associate-/r*_binary64_1399
12×sqrt-div_binary64_1472
cbrt-unprod_binary64_1488
pow1_binary64_1516 1-exp_binary64_1499 add-log-exp_binary64_1494
associate-/l/_binary64_1402
clear-num_binary64_1454 frac-2neg_binary64_1466 div-sub_binary64_1460
associate-*r/_binary64_1397 frac-times_binary64_1465 *-commutative_binary64_1386 sum-log_binary64_1546 +-commutative_binary64_1385 associate-*l/_binary64_1398 pow-prod-down_binary64_1526
Counts
4 → 589
Calls

4 calls:

283.0ms
(*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1))
26.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
14.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
6.0ms
(+.f64 1 (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))

series1.7s (8.1%)

Counts
4 → 12
Calls

4 calls:

549.0ms
(*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1))
478.0ms
(+.f64 1 (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))
363.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
283.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify280.0ms (1.4%)

Algorithm
egg-herbie
Counts
601 → 601
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0504935244

prune3.9s (19%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New5965601
Fresh459
Picked101
Done112
Total60211613

Merged error: 7.0b

Counts
613 → 11
Compiler

Compiled 55727 to 34330 computations (38.4% saved)

regimes197.0ms (1%)

Compiler

Compiled 2612 to 1780 computations (31.9% saved)

bsearch40.0ms (0.2%)

Steps
ItersRangePoint
9
1.3426077237192295e+101
4.2466070356158536e+110
3.609134889052862e+103
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06593
16593

end0.0ms (0%)

sample1.6s (7.7%)

Algorithm
intervals
Results
383.0ms6479×body128valid
193.0ms8000×pre128true
153.0ms657×body1024valid
89.0ms498×body512valid
39.0ms308×body256valid
17.0ms58×body2048valid
Compiler

Compiled 751 to 512 computations (31.8% saved)

Profiling

Loading profile data...