Details

Time bar (total: 10.0min)

analyze4.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%56.2%43.8%0
0%56.2%43.8%1
0%56.2%43.8%2
42.1%14%43.8%3
42.1%14%43.8%4
52.7%3.5%43.8%5
56.2%0%43.8%6
Compiler

Compiled 42 to 29 computations (31% saved)

sample31.0ms (0%)

Algorithm
intervals
Results
14.0ms256×body128valid
4.0ms256×pre128true
Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify664.0ms (0.1%)

Algorithm
egg-herbie
Rules
719×distribute-rgt-in_binary64_1392
695×distribute-lft-in_binary64_1391
516×associate-*l*_binary64_1383
478×exp-prod_binary64_1494
475×distribute-rgt-out--_binary64_1396
382×associate-+r+_binary64_1374
377×associate-+l+_binary64_1375
258×associate-*r*_binary64_1382
245×pow-plus_binary64_1505
240×associate-/l*_binary64_1387
161×times-frac_binary64_1448
133×sqr-pow_binary64_1414
120×associate-/l/_binary64_1389
115×cancel-sign-sub-inv_binary64_1408
112×pow-sqr_binary64_1415
105×pow-base-1_binary64_1502
93×*-commutative_binary64_1373
72×distribute-rgt-neg-in_binary64_1400
71×associate-/r*_binary64_1386
68×associate-*l/_binary64_1385
65×sub-neg_binary64_1435
64×associate--l+_binary64_1379
47×associate--r+_binary64_1378
38×distribute-rgt1-in_binary64_1398 distribute-rgt-out_binary64_1395
35×*-lft-identity_binary64_1431
31×remove-double-div_binary64_1418 distribute-lft-neg-in_binary64_1399 associate-/r/_binary64_1388
27×*-rgt-identity_binary64_1432
23×+-commutative_binary64_1372
17×associate-*r/_binary64_1384
14×distribute-neg-frac_binary64_1406
13×prod-exp_binary64_1491
12×/-rgt-identity_binary64_1433 swap-sqr_binary64_1409 distribute-lft1-in_binary64_1397
div-exp_binary64_1493 neg-mul-1_binary64_1438 neg-sub0_binary64_1437
+-inverses_binary64_1421 distribute-neg-in_binary64_1403
exp-lft-sqr_binary64_1497 exp-sum_binary64_1488 cube-prod_binary64_1470 unswap-sqr_binary64_1410
cube-div_binary64_1471
cube-unmult_binary64_1479
unpow3_binary64_1508 exp-sqrt_binary64_1495 rec-exp_binary64_1492 count-2_binary64_1390
1-exp_binary64_1486 exp-1-e_binary64_1485 cube-mult_binary64_1472 rem-sqrt-square_binary64_1455 --rgt-identity_binary64_1428 +-rgt-identity_binary64_1427 div0_binary64_1423 *-inverses_binary64_1422 rgt-mult-inverse_binary64_1419 difference-of-sqr-1_binary64_1412 difference-of-squares_binary64_1411
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64_1705 erf-erfc_binary64_1704 erf-odd_binary64_1703 if-if-and-not_binary64_1702 if-if-and_binary64_1701 if-if-or-not_binary64_1700 if-if-or_binary64_1699 if-not_binary64_1698 if-same_binary64_1697 if-false_binary64_1696 if-true_binary64_1695 not-gte_binary64_1694 not-lte_binary64_1693 not-gt_binary64_1692 not-lt_binary64_1691 gte-same_binary64_1690 lte-same_binary64_1689 gt-same_binary64_1688 lt-same_binary64_1687 sinh---cosh_binary64_1634 sinh-+-cosh_binary64_1633 sinh-cosh_binary64_1632 tanh-def-c_binary64_1631 tanh-def-b_binary64_1630 tanh-def-a_binary64_1629 cosh-def_binary64_1628 sinh-def_binary64_1627 tan-neg_binary64_1574 cos-neg_binary64_1573 sin-neg_binary64_1572 tan-0_binary64_1571 cos-0_binary64_1570 sin-0_binary64_1569 hang-m-tan_binary64_1568 hang-p-tan_binary64_1567 hang-m0-tan_binary64_1566 hang-p0-tan_binary64_1565 hang-0m-tan_binary64_1564 hang-0p-tan_binary64_1563 tan-+PI/2_binary64_1562 tan-+PI_binary64_1561 tan-PI_binary64_1560 tan-PI/3_binary64_1559 tan-PI/4_binary64_1558 tan-PI/6_binary64_1557 cos-+PI/2_binary64_1556 cos-+PI_binary64_1555 cos-PI_binary64_1554 cos-PI/2_binary64_1553 cos-PI/3_binary64_1552 cos-PI/4_binary64_1551 cos-PI/6_binary64_1550 sin-+PI/2_binary64_1549 sin-+PI_binary64_1548 sin-PI_binary64_1547 sin-PI/2_binary64_1546 sin-PI/3_binary64_1545 sin-PI/4_binary64_1544 sin-PI/6_binary64_1543 sub-1-sin_binary64_1542 sub-1-cos_binary64_1541 -1-add-sin_binary64_1540 -1-add-cos_binary64_1539 1-sub-sin_binary64_1538 1-sub-cos_binary64_1537 cos-sin-sum_binary64_1536 log-E_binary64_1532 log-pow_binary64_1531 log-rec_binary64_1530 log-div_binary64_1529 log-prod_binary64_1528 pow-base-0_binary64_1526 unpow1/3_binary64_1509 unpow2_binary64_1507 unpow1/2_binary64_1506 exp-to-pow_binary64_1504 unpow0_binary64_1501 unpow1_binary64_1500 unpow-1_binary64_1499 exp-lft-cube_binary64_1498 exp-cbrt_binary64_1496 exp-diff_binary64_1490 exp-neg_binary64_1489 e-exp-1_binary64_1487 exp-0_binary64_1484 rem-log-exp_binary64_1483 rem-exp-log_binary64_1482 cube-neg_binary64_1469 rem-3cbrt-rft_binary64_1468 rem-3cbrt-lft_binary64_1467 rem-cbrt-cube_binary64_1466 rem-cube-cbrt_binary64_1465 sqr-abs_binary64_1457 sqr-neg_binary64_1456 rem-square-sqrt_binary64_1454 div-sub_binary64_1447 unsub-neg_binary64_1436 mul-1-neg_binary64_1434 remove-double-neg_binary64_1430 sub0-neg_binary64_1429 +-lft-identity_binary64_1426 mul0-rgt_binary64_1425 mul0-lft_binary64_1424 lft-mult-inverse_binary64_1420 difference-of-sqr--1_binary64_1413 cancel-sign-sub_binary64_1407 distribute-frac-neg_binary64_1405 distribute-neg-out_binary64_1404 distribute-rgt-neg-out_binary64_1402 distribute-lft-neg-out_binary64_1401 distribute-lft-out--_binary64_1394 distribute-lft-out_binary64_1393 associate--r-_binary64_1381 associate--l-_binary64_1380 associate-+l-_binary64_1377 associate-+r-_binary64_1376
Counts
1 → 6
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01543
13643
211443
346840
4233040
5228040
6258440
7296640
8322240
9452440

prune19.0ms (0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New336
Fresh011
Picked000
Done000
Total347
Error
0.9b
Counts
7 → 4
Compiler

Compiled 286 to 195 computations (31.8% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))
0.0b
(/.f64 (+.f64 beta 1) (+.f64 beta (+.f64 1 (+.f64 alpha 2))))
0.1b
(*.f64 (/.f64 (+.f64 beta 1) (+.f64 beta (+.f64 1 (+.f64 alpha 2)))) (/.f64 (+.f64 alpha 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))))
11.6b
(/.f64 (+.f64 alpha 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2))))

rewrite713.0ms (0.1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
192×*-un-lft-identity_binary64_1442
94×distribute-lft-out_binary64_1393
60×times-frac_binary64_1448
47×add-sqr-sqrt_binary64_1464
35×add-cube-cbrt_binary64_1477 associate-*l*_binary64_1383
34×add-exp-log_binary64_1480 add-cbrt-cube_binary64_1478
22×flip3-+_binary64_1445 flip-+_binary64_1416
21×associate-*r*_binary64_1382
20×associate-/r/_binary64_1388
13×pow1_binary64_1503 frac-times_binary64_1452
11×swap-sqr_binary64_1409
10×prod-exp_binary64_1491 div-exp_binary64_1493 cbrt-undiv_binary64_1476 cbrt-unprod_binary64_1475
associate-/l*_binary64_1387
associate-*l/_binary64_1385 associate-*r/_binary64_1384 associate-/r*_binary64_1386
unswap-sqr_binary64_1410
add-log-exp_binary64_1481 div-inv_binary64_1439 associate-/l/_binary64_1389
frac-2neg_binary64_1453 clear-num_binary64_1441 pow-prod-down_binary64_1513 *-commutative_binary64_1373
pow2_binary64_1523 pow-prod-up_binary64_1512 pow-plus_binary64_1505 pow-sqr_binary64_1415 distribute-rgt-in_binary64_1392 distribute-lft-in_binary64_1391
Counts
4 → 204
Calls

4 calls:

40.0ms
(*.f64 (/.f64 (+.f64 beta 1) (+.f64 beta (+.f64 1 (+.f64 alpha 2)))) (/.f64 (+.f64 alpha 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))))
15.0ms
(/.f64 (+.f64 alpha 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2))))
13.0ms
(*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))
12.0ms
(/.f64 (+.f64 beta 1) (+.f64 beta (+.f64 1 (+.f64 alpha 2))))
Compiler

Compiled 8203 to 5917 computations (27.9% saved)

series3.1s (0.5%)

Error
0.7b
Counts
4 → 90
Calls

4 calls:

1.6s
(*.f64 (/.f64 (+.f64 beta 1) (+.f64 beta (+.f64 1 (+.f64 alpha 2)))) (/.f64 (+.f64 alpha 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))))
575.0ms
(/.f64 (+.f64 alpha 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2))))
243.0ms
(/.f64 (+.f64 beta 1) (+.f64 beta (+.f64 1 (+.f64 alpha 2))))
187.0ms
(*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))
Compiler

Compiled 15454 to 12240 computations (20.8% saved)

simplify4.0s (0.7%)

Algorithm
egg-herbie
Rules
366×distribute-rgt-in_binary64_1392
339×distribute-lft-in_binary64_1391
313×+-commutative_binary64_1372
247×*-commutative_binary64_1373
238×associate-+r+_binary64_1374
183×associate-*r/_binary64_1384
169×sub-neg_binary64_1435
113×distribute-neg-in_binary64_1403
110×associate-/r*_binary64_1386
92×cancel-sign-sub-inv_binary64_1408
85×associate-/l*_binary64_1387
84×unswap-sqr_binary64_1410
68×times-frac_binary64_1448
53×sqr-pow_binary64_1414
48×neg-mul-1_binary64_1438 neg-sub0_binary64_1437
38×associate--r+_binary64_1378
34×associate--l+_binary64_1379
31×associate-*l/_binary64_1385
25×*-rgt-identity_binary64_1432
21×pow-sqr_binary64_1415
18×associate-*r*_binary64_1382
17×distribute-rgt-neg-in_binary64_1400
15×swap-sqr_binary64_1409 associate-*l*_binary64_1383
13×distribute-rgt-out_binary64_1395
12×cube-unmult_binary64_1479
11×distribute-lft-neg-in_binary64_1399
unpow2_binary64_1507 exp-prod_binary64_1494
log-div_binary64_1529 log-prod_binary64_1528 distribute-rgt-out--_binary64_1396
*-lft-identity_binary64_1431 difference-of-squares_binary64_1411
unpow3_binary64_1508 pow-plus_binary64_1505 cube-mult_binary64_1472 associate-+r-_binary64_1376
exp-sum_binary64_1488 cube-prod_binary64_1470 /-rgt-identity_binary64_1433 distribute-lft-neg-out_binary64_1401
unsub-neg_binary64_1436 distribute-neg-frac_binary64_1406 distribute-rgt1-in_binary64_1398
rem-sqrt-square_binary64_1455 count-2_binary64_1390
div-exp_binary64_1493 rec-exp_binary64_1492 prod-exp_binary64_1491 1-exp_binary64_1486 rem-3cbrt-rft_binary64_1468 rem-3cbrt-lft_binary64_1467 rem-square-sqrt_binary64_1454 *-inverses_binary64_1422 distribute-lft-out_binary64_1393 associate-+l-_binary64_1377
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64_1705 erf-erfc_binary64_1704 erf-odd_binary64_1703 if-if-and-not_binary64_1702 if-if-and_binary64_1701 if-if-or-not_binary64_1700 if-if-or_binary64_1699 if-not_binary64_1698 if-same_binary64_1697 if-false_binary64_1696 if-true_binary64_1695 not-gte_binary64_1694 not-lte_binary64_1693 not-gt_binary64_1692 not-lt_binary64_1691 gte-same_binary64_1690 lte-same_binary64_1689 gt-same_binary64_1688 lt-same_binary64_1687 sinh---cosh_binary64_1634 sinh-+-cosh_binary64_1633 sinh-cosh_binary64_1632 tanh-def-c_binary64_1631 tanh-def-b_binary64_1630 tanh-def-a_binary64_1629 cosh-def_binary64_1628 sinh-def_binary64_1627 tan-neg_binary64_1574 cos-neg_binary64_1573 sin-neg_binary64_1572 tan-0_binary64_1571 cos-0_binary64_1570 sin-0_binary64_1569 hang-m-tan_binary64_1568 hang-p-tan_binary64_1567 hang-m0-tan_binary64_1566 hang-p0-tan_binary64_1565 hang-0m-tan_binary64_1564 hang-0p-tan_binary64_1563 tan-+PI/2_binary64_1562 tan-+PI_binary64_1561 tan-PI_binary64_1560 tan-PI/3_binary64_1559 tan-PI/4_binary64_1558 tan-PI/6_binary64_1557 cos-+PI/2_binary64_1556 cos-+PI_binary64_1555 cos-PI_binary64_1554 cos-PI/2_binary64_1553 cos-PI/3_binary64_1552 cos-PI/4_binary64_1551 cos-PI/6_binary64_1550 sin-+PI/2_binary64_1549 sin-+PI_binary64_1548 sin-PI_binary64_1547 sin-PI/2_binary64_1546 sin-PI/3_binary64_1545 sin-PI/4_binary64_1544 sin-PI/6_binary64_1543 sub-1-sin_binary64_1542 sub-1-cos_binary64_1541 -1-add-sin_binary64_1540 -1-add-cos_binary64_1539 1-sub-sin_binary64_1538 1-sub-cos_binary64_1537 cos-sin-sum_binary64_1536 log-E_binary64_1532 log-pow_binary64_1531 log-rec_binary64_1530 pow-base-0_binary64_1526 unpow1/3_binary64_1509 unpow1/2_binary64_1506 exp-to-pow_binary64_1504 pow-base-1_binary64_1502 unpow0_binary64_1501 unpow1_binary64_1500 unpow-1_binary64_1499 exp-lft-cube_binary64_1498 exp-lft-sqr_binary64_1497 exp-cbrt_binary64_1496 exp-sqrt_binary64_1495 exp-diff_binary64_1490 exp-neg_binary64_1489 e-exp-1_binary64_1487 exp-1-e_binary64_1485 exp-0_binary64_1484 rem-log-exp_binary64_1483 rem-exp-log_binary64_1482 cube-div_binary64_1471 cube-neg_binary64_1469 rem-cbrt-cube_binary64_1466 rem-cube-cbrt_binary64_1465 sqr-abs_binary64_1457 sqr-neg_binary64_1456 div-sub_binary64_1447 mul-1-neg_binary64_1434 remove-double-neg_binary64_1430 sub0-neg_binary64_1429 --rgt-identity_binary64_1428 +-rgt-identity_binary64_1427 +-lft-identity_binary64_1426 mul0-rgt_binary64_1425 mul0-lft_binary64_1424 div0_binary64_1423 +-inverses_binary64_1421 lft-mult-inverse_binary64_1420 rgt-mult-inverse_binary64_1419 remove-double-div_binary64_1418 difference-of-sqr--1_binary64_1413 difference-of-sqr-1_binary64_1412 cancel-sign-sub_binary64_1407 distribute-frac-neg_binary64_1405 distribute-neg-out_binary64_1404 distribute-rgt-neg-out_binary64_1402 distribute-lft1-in_binary64_1397 distribute-lft-out--_binary64_1394 associate-/l/_binary64_1389 associate-/r/_binary64_1388 associate--r-_binary64_1381 associate--l-_binary64_1380 associate-+l+_binary64_1375
Counts
294 → 490
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0100016898
1333615360

prune3.0s (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New4873490
Fresh123
Picked011
Done000
Total4886494
Error
0b
Counts
494 → 6
Compiler

Compiled 27453 to 19525 computations (28.9% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha))) (cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha))))
7.7b
(cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha)))
7.7b
(cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha)))
7.7b
(cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha)))

rewrite25.5s (4.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
8237×*-un-lft-identity_binary64_1442
4210×times-frac_binary64_1448
3783×distribute-lft-out_binary64_1393
2300×cbrt-prod_binary64_1473
991×add-sqr-sqrt_binary64_1464
935×add-cube-cbrt_binary64_1477
801×swap-sqr_binary64_1409
139×associate-*l*_binary64_1383 associate-*r*_binary64_1382
108×associate-/r/_binary64_1388
54×div-inv_binary64_1439 flip3-+_binary64_1445 flip-+_binary64_1416
16×unswap-sqr_binary64_1410
11×pow1_binary64_1503
pow1/3_binary64_1524
cbrt-div_binary64_1474
add-exp-log_binary64_1480
add-log-exp_binary64_1481 add-cbrt-cube_binary64_1478
pow-prod-down_binary64_1513 pow-prod-up_binary64_1512 pow-sqr_binary64_1415
pow2_binary64_1523 pow-plus_binary64_1505 prod-exp_binary64_1491 cbrt-unprod_binary64_1475 frac-times_binary64_1452 associate-*l/_binary64_1385 associate-*r/_binary64_1384 *-commutative_binary64_1373
Counts
4 → 1551
Calls

4 calls:

318.0ms
(*.f64 (cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha))) (cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha))))
27.0ms
(cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha)))
23.0ms
(cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha)))
23.0ms
(cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha)))
Compiler

Compiled 130468 to 96925 computations (25.7% saved)

series9.4min (93.8%)

Calls

3 calls:

7.7s
(cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha)))
7.7s
(cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha)))
7.7s
(cbrt.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 2 beta) alpha)) (+.f64 (+.f64 2 beta) alpha)))
Compiler

Compiled 31556 to 26351 computations (16.5% saved)

Profiling

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