Details

analyze338.0ms (1.1%)

Algorithm

1×	search
2×	egg-herbie

Rules

478×	`sub-neg_binary64_1435`
434×	`distribute-rgt-in_binary64_1392` `associate-+l+_binary64_1375`
406×	`associate-l_binary64_1383`
374×	`associate-+r+_binary64_1374`
354×	`associate--l+_binary64_1379`
350×	`*-commutative_binary64_1373`
326×	`associate-r_binary64_1382`
291×	`distribute-lft-in_binary64_1391`
286×	`distribute-rgt-out_binary64_1395`
280×	`neg-mul-1_binary64_1438`
244×	`unsub-neg_binary64_1436`
194×	`neg-sub0_binary64_1437`
142×	`associate-+l-_binary64_1377`
130×	`+-commutative_binary64_1372`
119×	`distribute-rgt-neg-out_binary64_1402`
118×	`distribute-lft-neg-out_binary64_1401`
112×	`distribute-lft-out_binary64_1393`
93×	`cancel-sign-sub-inv_binary64_1408`
84×	`associate-+r-_binary64_1376`
58×	`associate--r+_binary64_1378`
40×	`distribute-rgt-neg-in_binary64_1400`
38×	`unswap-sqr_binary64_1410`
29×	`distribute-lft-neg-in_binary64_1399`
22×	`associate--r-_binary64_1381`
20×	`*-rgt-identity_binary64_1432`
19×	`*-lft-identity_binary64_1431`
18×	`distribute-neg-in_binary64_1403`
14×	`sqr-pow_binary64_1414`
8×	`difference-of-sqr--1_binary64_1413`
7×	`pow-plus_binary64_1505`
6×	`mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `swap-sqr_binary64_1409` `distribute-lft1-in_binary64_1397`
5×	`cube-unmult_binary64_1479`
4×	`difference-of-sqr-1_binary64_1412`
2×	`unpow2_binary64_1507` `mul-1-neg_binary64_1434` `sub0-neg_binary64_1429`
1×	`unpow3_binary64_1508` `unpow1/2_binary64_1506` `unpow1_binary64_1500` `1-exp_binary64_1486` `cube-prod_binary64_1470` `rem-sqrt-square_binary64_1455` `distribute-rgt1-in_binary64_1398`
0×	`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` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `exp-prod_binary64_1494` `div-exp_binary64_1493` `rec-exp_binary64_1492` `prod-exp_binary64_1491` `exp-diff_binary64_1490` `exp-neg_binary64_1489` `exp-sum_binary64_1488` `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-mult_binary64_1472` `cube-div_binary64_1471` `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` `times-frac_binary64_1448` `div-sub_binary64_1447` `/-rgt-identity_binary64_1433` `remove-double-neg_binary64_1430` `--rgt-identity_binary64_1428` `+-rgt-identity_binary64_1427` `+-lft-identity_binary64_1426` `div0_binary64_1423` `-inverses_binary64_1422` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `remove-double-div_binary64_1418` `pow-sqr_binary64_1415` `difference-of-squares_binary64_1411` `cancel-sign-sub_binary64_1407` `distribute-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-rgt-out--_binary64_1396` `distribute-lft-out--_binary64_1394` `count-2_binary64_1390` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `associate-/l_binary64_1387` `associate-/r_binary64_1386` `associate-l/_binary64_1385` `associate-*r/_binary64_1384` `associate--l-_binary64_1380`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	92
1	100	92
2	254	92
3	765	92
4	2201	92
5	4207	92
6	4979	92
7	5012	92
0	2	2
1	2	2

Search

True	Other	False	Iter
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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 22 computations (31.3% saved)

sample26.0ms (0.1%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify60.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

669×	`unsub-neg_binary64_1436`
596×	`cancel-sign-sub-inv_binary64_1408`
373×	`neg-mul-1_binary64_1438` `neg-sub0_binary64_1437`
340×	`+-commutative_binary64_1372`
277×	`sub-neg_binary64_1435`
242×	`distribute-rgt-neg-in_binary64_1400`
232×	`associate-+l+_binary64_1375`
220×	`*-commutative_binary64_1373`
212×	`associate-l_binary64_1383`
192×	`associate-+r+_binary64_1374`
188×	`associate--l+_binary64_1379`
185×	`associate-r_binary64_1382`
174×	`distribute-rgt-in_binary64_1392`
149×	`distribute-rgt-out_binary64_1395`
147×	`distribute-lft-in_binary64_1391`
146×	`distribute-neg-in_binary64_1403`
134×	`distribute-lft-neg-out_binary64_1401`
113×	`distribute-rgt-neg-out_binary64_1402`
84×	`unswap-sqr_binary64_1410`
72×	`associate-+l-_binary64_1377`
66×	`cancel-sign-sub_binary64_1407`
45×	`associate-+r-_binary64_1376`
38×	`distribute-lft-out_binary64_1393` `associate--r+_binary64_1378`
27×	`*-rgt-identity_binary64_1432`
26×	`distribute-lft-neg-in_binary64_1399`
20×	`*-lft-identity_binary64_1431`
19×	`sqr-pow_binary64_1414`
11×	`associate--r-_binary64_1381`
10×	`sub0-neg_binary64_1429`
9×	`pow-plus_binary64_1505` `mul0-rgt_binary64_1425` `mul0-lft_binary64_1424`
8×	`+-rgt-identity_binary64_1427` `difference-of-sqr--1_binary64_1413`
6×	`cube-unmult_binary64_1479` `swap-sqr_binary64_1409`
5×	`rem-sqrt-square_binary64_1455` `difference-of-sqr-1_binary64_1412` `distribute-lft1-in_binary64_1397`
4×	`distribute-neg-out_binary64_1404`
3×	`unpow2_binary64_1507` `cube-prod_binary64_1470`
2×	`mul-1-neg_binary64_1434`
1×	`unpow3_binary64_1508` `unpow1/2_binary64_1506` `unpow1_binary64_1500` `1-exp_binary64_1486` `remove-double-neg_binary64_1430` `--rgt-identity_binary64_1428` `pow-sqr_binary64_1415` `distribute-rgt1-in_binary64_1398`
0×	`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` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `exp-prod_binary64_1494` `div-exp_binary64_1493` `rec-exp_binary64_1492` `prod-exp_binary64_1491` `exp-diff_binary64_1490` `exp-neg_binary64_1489` `exp-sum_binary64_1488` `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-mult_binary64_1472` `cube-div_binary64_1471` `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` `times-frac_binary64_1448` `div-sub_binary64_1447` `/-rgt-identity_binary64_1433` `+-lft-identity_binary64_1426` `div0_binary64_1423` `-inverses_binary64_1422` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `remove-double-div_binary64_1418` `difference-of-squares_binary64_1411` `distribute-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-rgt-out--_binary64_1396` `distribute-lft-out--_binary64_1394` `count-2_binary64_1390` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `associate-/l_binary64_1387` `associate-/r_binary64_1386` `associate-l/_binary64_1385` `associate-*r/_binary64_1384` `associate--l-_binary64_1380`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	46
1	61	46
2	152	46
3	438	46
4	1297	46
5	2508	46
6	4605	46
7	5029	46

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.2b

Counts

2 → 1

Compiler

Compiled 62 to 42 computations (32.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.0b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.0b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite199.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`pow1_binary64_1503` `add-exp-log_binary64_1480`
14×	`add-cbrt-cube_binary64_1478`
10×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
8×	`add-cube-cbrt_binary64_1477`
7×	`associate-r_binary64_1382`
6×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `add-log-exp_binary64_1481` `cbrt-unprod_binary64_1475`
4×	`distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `associate-*r/_binary64_1384`
3×	`unpow-prod-down_binary64_1521` `pow-unpow_binary64_1519`
2×	`unswap-sqr_binary64_1410` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408` `associate-l_binary64_1383` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-+r+_binary64_1374`
1×	`flip3--_binary64_1446` `flip--_binary64_1417` `pow-pow_binary64_1514` `pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `unpow2_binary64_1507` `sqr-pow_binary64_1414` `distribute-lft-out_binary64_1393` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 80

Calls

4 calls:

9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
9.0ms	(.f64 (.f64 a a) (+.f64 1 a))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 3307 to 1781 computations (46.1% saved)

series1.1s (3.7%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

563.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
287.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
135.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
74.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 3720 to 2815 computations (24.3% saved)

simplify88.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

853×	`distribute-rgt-in_binary64_1392`
794×	`distribute-lft-in_binary64_1391`
274×	`cancel-sign-sub-inv_binary64_1408`
246×	`associate-l_binary64_1383`
204×	`associate-r_binary64_1382`
122×	`distribute-rgt-neg-in_binary64_1400`
109×	`*-commutative_binary64_1373`
104×	`distribute-lft-neg-in_binary64_1399`
95×	`unswap-sqr_binary64_1410`
85×	`distribute-rgt-out_binary64_1395`
71×	`+-commutative_binary64_1372`
69×	`sqr-pow_binary64_1414`
63×	`exp-prod_binary64_1494`
58×	`associate-+r+_binary64_1374`
55×	`distribute-lft-out_binary64_1393`
49×	`associate-+l+_binary64_1375`
43×	`sub-neg_binary64_1435`
42×	`log-prod_binary64_1528`
36×	`associate--l+_binary64_1379`
35×	`distribute-neg-in_binary64_1403`
31×	`distribute-lft-neg-out_binary64_1401`
29×	`neg-sub0_binary64_1437`
28×	`neg-mul-1_binary64_1438` `*-lft-identity_binary64_1431`
27×	`exp-sum_binary64_1488`
23×	`cube-prod_binary64_1470`
22×	`*-rgt-identity_binary64_1432`
20×	`distribute-rgt-out--_binary64_1396`
19×	`swap-sqr_binary64_1409` `distribute-rgt-neg-out_binary64_1402`
12×	`cube-unmult_binary64_1479` `pow-sqr_binary64_1415`
9×	`pow-plus_binary64_1505` `unsub-neg_binary64_1436`
8×	`distribute-lft-out--_binary64_1394`
7×	`log-pow_binary64_1531`
6×	`unpow3_binary64_1508` `unpow2_binary64_1507` `unpow1/2_binary64_1506` `unpow1_binary64_1500`
5×	`cube-mult_binary64_1472`
2×	`exp-diff_binary64_1490` `rem-sqrt-square_binary64_1455` `distribute-rgt1-in_binary64_1398` `count-2_binary64_1390` `associate--r+_binary64_1378`
1×	`prod-exp_binary64_1491` `1-exp_binary64_1486` `exp-1-e_binary64_1485` `rem-3cbrt-rft_binary64_1468` `rem-square-sqrt_binary64_1454` `div-sub_binary64_1447` `difference-of-squares_binary64_1411` `associate-/l*_binary64_1387` `associate-+l-_binary64_1377` `associate-+r-_binary64_1376`
0×	`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-rec_binary64_1530` `log-div_binary64_1529` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `div-exp_binary64_1493` `rec-exp_binary64_1492` `exp-neg_binary64_1489` `e-exp-1_binary64_1487` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `cube-div_binary64_1471` `cube-neg_binary64_1469` `rem-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `times-frac_binary64_1448` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `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_1422` `+-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-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-lft1-in_binary64_1397` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `associate-/r_binary64_1386` `associate-l/_binary64_1385` `associate-r/_binary64_1384` `associate--r-_binary64_1381` `associate--l-_binary64_1380`

Counts

133 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	3004
1	533	2688
2	1756	2603
3	5452	2603

prune195.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	2	106

Error

0.0b

Counts

106 → 2

Compiler

Compiled 3715 to 2017 computations (45.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))
0.0b	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
0.6b	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a))))
1.1b	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

rewrite305.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`add-log-exp_binary64_1481`
14×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
8×	`add-sqr-sqrt_binary64_1464` `associate-*r/_binary64_1384`
7×	`sum-log_binary64_1533`
6×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `add-cube-cbrt_binary64_1477` `cbrt-unprod_binary64_1475` `-un-lft-identity_binary64_1442` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `associate-r*_binary64_1382`
5×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
4×	`sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408` `frac-add_binary64_1450` `associate-+r+_binary64_1374`
3×	`flip3--_binary64_1446` `flip--_binary64_1417` `associate-+l+_binary64_1375`
2×	`unswap-sqr_binary64_1410` `associate-l_binary64_1383` `*-commutative_binary64_1373` `+-commutative_binary64_1372`

Counts

4 → 83

Calls

4 calls:

21.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
16.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))
12.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a))))
8.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 4584 to 2940 computations (35.9% saved)

series1.6s (5.1%)

Error

0.0b

Counts

4 → 56

Calls

4 calls:

567.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
480.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))
295.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a))))
155.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 4241 to 3406 computations (19.7% saved)

simplify194.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

501×	`cancel-sign-sub-inv_binary64_1408`
396×	`associate-l_binary64_1383`
356×	`associate-r_binary64_1382`
252×	`distribute-rgt-neg-in_binary64_1400`
226×	`distribute-rgt-in_binary64_1392`
221×	`*-commutative_binary64_1373`
213×	`distribute-lft-in_binary64_1391`
173×	`unswap-sqr_binary64_1410`
108×	`+-commutative_binary64_1372`
104×	`distribute-neg-in_binary64_1403`
99×	`sub-neg_binary64_1435`
86×	`associate-+l+_binary64_1375`
83×	`associate-+r+_binary64_1374`
80×	`exp-prod_binary64_1494`
76×	`sqr-pow_binary64_1414`
71×	`distribute-lft-neg-out_binary64_1401`
61×	`exp-sum_binary64_1488`
60×	`cube-prod_binary64_1470`
52×	`neg-sub0_binary64_1437`
51×	`neg-mul-1_binary64_1438`
47×	`distribute-rgt-neg-out_binary64_1402`
46×	`associate--l+_binary64_1379`
42×	`log-prod_binary64_1528`
38×	`swap-sqr_binary64_1409`
35×	`distribute-lft-neg-in_binary64_1399`
29×	`unpow3_binary64_1508`
28×	`unsub-neg_binary64_1436`
27×	`*-rgt-identity_binary64_1432` `distribute-rgt-out_binary64_1395`
26×	`*-lft-identity_binary64_1431`
17×	`pow-plus_binary64_1505`
16×	`cube-mult_binary64_1472`
15×	`associate--r+_binary64_1378`
12×	`prod-exp_binary64_1491`
11×	`distribute-lft-out_binary64_1393`
8×	`pow-sqr_binary64_1415` `distribute-rgt-out--_binary64_1396`
7×	`difference-of-squares_binary64_1411`
6×	`log-pow_binary64_1531` `exp-lft-sqr_binary64_1497`
4×	`unpow1/2_binary64_1506` `exp-diff_binary64_1490` `distribute-lft-out--_binary64_1394`
3×	`associate-+l-_binary64_1377` `associate-+r-_binary64_1376`
2×	`unpow2_binary64_1507` `unpow1_binary64_1500` `cube-unmult_binary64_1479` `count-2_binary64_1390`
1×	`1-exp_binary64_1486` `exp-1-e_binary64_1485` `div-sub_binary64_1447` `distribute-lft1-in_binary64_1397`
0×	`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-rec_binary64_1530` `log-div_binary64_1529` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `div-exp_binary64_1493` `rec-exp_binary64_1492` `exp-neg_binary64_1489` `e-exp-1_binary64_1487` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `cube-div_binary64_1471` `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-sqrt-square_binary64_1455` `rem-square-sqrt_binary64_1454` `times-frac_binary64_1448` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `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_1422` `+-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-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-rgt1-in_binary64_1398` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `associate-/l_binary64_1387` `associate-/r_binary64_1386` `associate-l/_binary64_1385` `associate-*r/_binary64_1384` `associate--r-_binary64_1381` `associate--l-_binary64_1380`

Counts

139 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	4842
1	772	4515
2	3139	4497
3	4977	4497
4	4995	4497
5	4931	4497

prune295.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	118	3	121

Error

0.0b

Counts

121 → 3

Compiler

Compiled 5219 to 3396 computations (34.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 a (+.f64 a (.f64 a a))) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 a (+.f64 a (.f64 a a)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.0b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite171.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464`
11×	`add-cbrt-cube_binary64_1478`
10×	`*-un-lft-identity_binary64_1442`
9×	`add-cube-cbrt_binary64_1477`
8×	`associate-r_binary64_1382`
6×	`add-log-exp_binary64_1481`
4×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `associate-r/_binary64_1384` `associate-l*_binary64_1383`
3×	`unpow-prod-down_binary64_1521` `pow-unpow_binary64_1519`
2×	`unswap-sqr_binary64_1410` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-+r+_binary64_1374`
1×	`flip3--_binary64_1446` `flip--_binary64_1417` `pow-pow_binary64_1514` `pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `unpow2_binary64_1507` `sqr-pow_binary64_1414` `distribute-rgt1-in_binary64_1398` `distribute-rgt-out_binary64_1395` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 80

Calls

4 calls:

9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 a (+.f64 a (.f64 a a))) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
7.0ms	(.f64 a (+.f64 a (.f64 a a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 3313 to 1480 computations (55.3% saved)

series1.1s (3.5%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

543.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 a (+.f64 a (.f64 a a))) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
277.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
131.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
84.0ms	(.f64 a (+.f64 a (.f64 a a)))

Compiler

Compiled 3720 to 2701 computations (27.4% saved)

simplify91.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

859×	`distribute-rgt-in_binary64_1392`
806×	`distribute-lft-in_binary64_1391`
288×	`cancel-sign-sub-inv_binary64_1408`
245×	`associate-l_binary64_1383`
221×	`associate-r_binary64_1382`
130×	`distribute-rgt-neg-in_binary64_1400`
127×	`distribute-rgt-out_binary64_1395`
110×	`distribute-lft-neg-in_binary64_1399`
101×	`*-commutative_binary64_1373`
90×	`unswap-sqr_binary64_1410`
70×	`sqr-pow_binary64_1414`
68×	`+-commutative_binary64_1372`
62×	`exp-prod_binary64_1494`
56×	`associate-+r+_binary64_1374`
50×	`associate-+l+_binary64_1375`
48×	`distribute-lft-out_binary64_1393`
47×	`sub-neg_binary64_1435`
37×	`log-prod_binary64_1528`
36×	`associate--l+_binary64_1379`
35×	`distribute-neg-in_binary64_1403`
32×	`cube-prod_binary64_1470`
31×	`distribute-lft-neg-out_binary64_1401`
30×	`neg-sub0_binary64_1437`
29×	`neg-mul-1_binary64_1438`
27×	`exp-sum_binary64_1488` `distribute-rgt-out--_binary64_1396`
23×	`*-lft-identity_binary64_1431`
21×	`*-rgt-identity_binary64_1432` `swap-sqr_binary64_1409`
18×	`distribute-rgt-neg-out_binary64_1402`
14×	`distribute-rgt1-in_binary64_1398`
12×	`pow-sqr_binary64_1415`
11×	`cube-unmult_binary64_1479`
10×	`pow-plus_binary64_1505`
9×	`unsub-neg_binary64_1436`
8×	`distribute-lft-out--_binary64_1394`
7×	`log-pow_binary64_1531` `unpow3_binary64_1508`
6×	`unpow2_binary64_1507` `unpow1/2_binary64_1506` `unpow1_binary64_1500` `cube-mult_binary64_1472`
4×	`difference-of-squares_binary64_1411`
3×	`rem-sqrt-square_binary64_1455`
2×	`exp-diff_binary64_1490` `distribute-lft1-in_binary64_1397` `associate--r+_binary64_1378`
1×	`prod-exp_binary64_1491` `1-exp_binary64_1486` `exp-1-e_binary64_1485` `rem-3cbrt-rft_binary64_1468` `rem-square-sqrt_binary64_1454` `div-sub_binary64_1447` `count-2_binary64_1390` `associate-/l*_binary64_1387` `associate-+l-_binary64_1377` `associate-+r-_binary64_1376`
0×	`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-rec_binary64_1530` `log-div_binary64_1529` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `div-exp_binary64_1493` `rec-exp_binary64_1492` `exp-neg_binary64_1489` `e-exp-1_binary64_1487` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `cube-div_binary64_1471` `cube-neg_binary64_1469` `rem-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `times-frac_binary64_1448` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `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_1422` `+-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-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `associate-/r_binary64_1386` `associate-l/_binary64_1385` `associate-r/_binary64_1384` `associate--r-_binary64_1381` `associate--l-_binary64_1380`

Counts

133 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	3013
1	533	2700
2	1799	2633
3	5503	2633

prune167.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	103	3	106

Error

0.0b

Counts

106 → 3

Compiler

Compiled 3722 to 1840 computations (50.6% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b	(.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))) (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))))
1.7b	(.f64 (.f64 b b) (+.f64 16 (.f64 -144 (.f64 a a))))
2.3b	(+.f64 (.f64 (+.f64 4 (.f64 12 a)) (-.f64 (pow.f64 b 8) (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))) (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))))))) (.f64 (.f64 (.f64 b b) (+.f64 16 (.f64 -144 (.f64 a a)))) (-.f64 (pow.f64 b 4) (+.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 4)))))
35.0b	(/.f64 (+.f64 (.f64 (+.f64 4 (.f64 12 a)) (-.f64 (pow.f64 b 8) (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))) (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))))))) (.f64 (.f64 (.f64 b b) (+.f64 16 (.f64 -144 (.f64 a a)))) (-.f64 (pow.f64 b 4) (+.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 4))))) (.f64 (+.f64 4 (.f64 12 a)) (-.f64 (pow.f64 b 4) (+.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 4 a))))) (pow.f64 a 4)))))

rewrite7.8s (24.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

174×	`associate-*r/_binary64_1384`
136×	`frac-times_binary64_1452`
128×	`frac-add_binary64_1450`
108×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
99×	`flip3--_binary64_1446` `flip--_binary64_1417`
68×	`associate-*l/_binary64_1385`
66×	`associate-/l/_binary64_1389`
27×	`add-exp-log_binary64_1480`
19×	`add-cbrt-cube_binary64_1478`
14×	`add-sqr-sqrt_binary64_1464`
13×	`prod-exp_binary64_1491`
11×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391`
9×	`pow1_binary64_1503`
8×	`associate-/r/_binary64_1388` `cancel-sign-sub-inv_binary64_1408` `associate-+r+_binary64_1374` `associate-l_binary64_1383`
7×	`cbrt-unprod_binary64_1475`
6×	`add-log-exp_binary64_1481`
4×	`sub-neg_binary64_1435` `associate-+l+_binary64_1375` `unswap-sqr_binary64_1410` `associate-r_binary64_1382` `unpow-prod-down_binary64_1521`
3×	`times-frac_binary64_1448` `associate-/l*_binary64_1387` `pow-prod-down_binary64_1513`
2×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `*-commutative_binary64_1373` `pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `sqr-pow_binary64_1414`
1×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `associate-/r*_binary64_1386` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 244

Calls

4 calls:

47.0ms	(/.f64 (+.f64 (.f64 (+.f64 4 (.f64 12 a)) (-.f64 (pow.f64 b 8) (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))) (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))))))) (.f64 (.f64 (.f64 b b) (+.f64 16 (.f64 -144 (.f64 a a)))) (-.f64 (pow.f64 b 4) (+.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 4))))) (.f64 (+.f64 4 (.f64 12 a)) (-.f64 (pow.f64 b 4) (+.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 4 a))))) (pow.f64 a 4)))))
36.0ms	(.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))) (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))))
30.0ms	(+.f64 (.f64 (+.f64 4 (.f64 12 a)) (-.f64 (pow.f64 b 8) (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))) (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))))))) (.f64 (.f64 (.f64 b b) (+.f64 16 (.f64 -144 (.f64 a a)))) (-.f64 (pow.f64 b 4) (+.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 4)))))
8.0ms	(.f64 (.f64 b b) (+.f64 16 (.f64 -144 (.f64 a a))))

Compiler

Compiled 66813 to 43230 computations (35.3% saved)

series8.2s (26.2%)

Error

0.0b

Counts

4 → 62

Calls

4 calls:

6.9s	(/.f64 (+.f64 (.f64 (+.f64 4 (.f64 12 a)) (-.f64 (pow.f64 b 8) (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))) (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))))))) (.f64 (.f64 (.f64 b b) (+.f64 16 (.f64 -144 (.f64 a a)))) (-.f64 (pow.f64 b 4) (+.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 4))))) (.f64 (+.f64 4 (.f64 12 a)) (-.f64 (pow.f64 b 4) (+.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 4 a))))) (pow.f64 a 4)))))
558.0ms	(+.f64 (.f64 (+.f64 4 (.f64 12 a)) (-.f64 (pow.f64 b 8) (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))) (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))))))) (.f64 (.f64 (.f64 b b) (+.f64 16 (.f64 -144 (.f64 a a)))) (-.f64 (pow.f64 b 4) (+.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 4)))))
234.0ms	(.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))) (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))))
206.0ms	(.f64 (.f64 b b) (+.f64 16 (.f64 -144 (.f64 a a))))

Compiler

Compiled 18114 to 14275 computations (21.2% saved)

simplify701.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

511×	`times-frac_binary64_1448`
482×	`*-commutative_binary64_1373`
262×	`associate-r_binary64_1382`
249×	`associate-l_binary64_1383`
224×	`+-commutative_binary64_1372`
122×	`cancel-sign-sub-inv_binary64_1408`
111×	`associate-+r+_binary64_1374`
88×	`distribute-rgt-in_binary64_1392`
86×	`unswap-sqr_binary64_1410` `distribute-lft-in_binary64_1391`
72×	`sqr-pow_binary64_1414`
66×	`sub-neg_binary64_1435`
58×	`associate-*r/_binary64_1384`
56×	`associate-/r*_binary64_1386`
46×	`neg-sub0_binary64_1437`
45×	`neg-mul-1_binary64_1438` `associate-/l*_binary64_1387`
28×	`cube-prod_binary64_1470`
27×	`swap-sqr_binary64_1409`
19×	`unpow3_binary64_1508`
18×	`exp-prod_binary64_1494`
14×	`log-prod_binary64_1528` `cube-mult_binary64_1472`
10×	`associate--l+_binary64_1379`
8×	`unpow2_binary64_1507`
6×	`unpow1_binary64_1500` `cube-unmult_binary64_1479` `unsub-neg_binary64_1436` `difference-of-squares_binary64_1411` `associate--r+_binary64_1378`
4×	`exp-sum_binary64_1488` `pow-sqr_binary64_1415` `distribute-neg-in_binary64_1403`
3×	`distribute-rgt-out--_binary64_1396` `associate-+r-_binary64_1376`
2×	`log-div_binary64_1529` `mul-1-neg_binary64_1434` `*-rgt-identity_binary64_1432` `distribute-lft-neg-out_binary64_1401` `distribute-rgt-neg-in_binary64_1400` `distribute-rgt-out_binary64_1395` `count-2_binary64_1390`
1×	`log-pow_binary64_1531` `pow-plus_binary64_1505` `prod-exp_binary64_1491` `exp-diff_binary64_1490` `1-exp_binary64_1486` `rem-sqrt-square_binary64_1455` `distribute-rgt-neg-out_binary64_1402` `distribute-lft-neg-in_binary64_1399` `associate-*l/_binary64_1385` `associate-+l+_binary64_1375`
0×	`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-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` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `div-exp_binary64_1493` `rec-exp_binary64_1492` `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-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` `/-rgt-identity_binary64_1433` `-lft-identity_binary64_1431` `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_1422` `+-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-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-rgt1-in_binary64_1398` `distribute-lft1-in_binary64_1397` `distribute-lft-out--_binary64_1394` `distribute-lft-out_binary64_1393` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `associate--r-_binary64_1381` `associate--l-_binary64_1380` `associate-+l-_binary64_1377`

Counts

306 → 277

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1017	56149
1	3692	53549
2	5015	53549

prune6.1s (19.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	277	3	280

Error

0.0b

Counts

280 → 3

Compiler

Compiled 62041 to 40532 computations (34.7% saved)

regimes665.0ms (2.1%)

Accuracy

Total 0.1b remaining (93.4%)

Threshold costs 0.1b (93.4%)

Compiler

Compiled 10387 to 7314 computations (29.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64_1372`
5×	`*-commutative_binary64_1373`
2×	`neg-mul-1_binary64_1438` `neg-sub0_binary64_1437` `sub-neg_binary64_1435` `*-rgt-identity_binary64_1432`
1×	`1-exp_binary64_1486` `unsub-neg_binary64_1436` `distribute-rgt-neg-out_binary64_1402`
0×	`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` `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` `tan-0_binary64_1571` `cos-0_binary64_1570` `sin-0_binary64_1569` `unpow1_binary64_1500` `e-exp-1_binary64_1487` `exp-1-e_binary64_1485` `exp-0_binary64_1484` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `*-lft-identity_binary64_1431` `remove-double-neg_binary64_1430` `sub0-neg_binary64_1429` `--rgt-identity_binary64_1428` `+-rgt-identity_binary64_1427` `+-lft-identity_binary64_1426` `cancel-sign-sub-inv_binary64_1408` `cancel-sign-sub_binary64_1407` `distribute-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-neg-in_binary64_1403` `distribute-lft-neg-out_binary64_1401` `distribute-rgt-neg-in_binary64_1400` `distribute-lft-neg-in_binary64_1399`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	46
1	33	46
2	37	46
3	39	46
4	42	46
5	41	46
6	39	46

end0.0ms (0%)

sample1.9s (6.1%)

Algorithm

1×

intervals

Results

475.0ms	8000×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 1876 to 1333 computations (28.9% saved)

Details

analyze338.0ms (1.1%)

sample26.0ms (0.1%)

simplify60.0ms (0.2%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite199.0ms (0.6%)

series1.1s (3.7%)

simplify88.0ms (0.3%)

prune195.0ms (0.6%)

localize20.0ms (0.1%)

rewrite305.0ms (1%)

series1.6s (5.1%)

simplify194.0ms (0.6%)

prune295.0ms (0.9%)

localize16.0ms (0.1%)

rewrite171.0ms (0.5%)

series1.1s (3.5%)

simplify91.0ms (0.3%)

prune167.0ms (0.5%)

localize37.0ms (0.1%)

rewrite7.8s (24.7%)

series8.2s (26.2%)

simplify701.0ms (2.2%)

prune6.1s (19.2%)

regimes665.0ms (2.1%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.9s (6.1%)

Profiling