Details

analyze146.0ms (1.3%)

Algorithm

1×	search
2×	egg-herbie

Rules

8×	`sub-neg_binary64_1435`
5×	`+-commutative_binary64_1372`
3×	`sub0-neg_binary64_1429` `associate--r+_binary64_1378` `associate-+l-_binary64_1377` `*-commutative_binary64_1373`
2×	`neg-mul-1_binary64_1438` `--rgt-identity_binary64_1428` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391`
1×	`1-exp_binary64_1486` `neg-sub0_binary64_1437` `associate-l/_binary64_1385` `associate-r/_binary64_1384` `associate--l+_binary64_1379` `associate-+l+_binary64_1375` `associate-+r+_binary64_1374`
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` `unpow3_binary64_1508` `unpow2_binary64_1507` `unpow1/2_binary64_1506` `pow-plus_binary64_1505` `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-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-unmult_binary64_1479` `cube-mult_binary64_1472` `cube-div_binary64_1471` `cube-prod_binary64_1470` `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` `div-sub_binary64_1447` `unsub-neg_binary64_1436` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `-rgt-identity_binary64_1432` `-lft-identity_binary64_1431` `remove-double-neg_binary64_1430` `+-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` `pow-sqr_binary64_1415` `sqr-pow_binary64_1414` `difference-of-sqr--1_binary64_1413` `difference-of-sqr-1_binary64_1412` `difference-of-squares_binary64_1411` `unswap-sqr_binary64_1410` `swap-sqr_binary64_1409` `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-rgt-neg-out_binary64_1402` `distribute-lft-neg-out_binary64_1401` `distribute-rgt-neg-in_binary64_1400` `distribute-lft-neg-in_binary64_1399` `distribute-rgt1-in_binary64_1398` `distribute-lft1-in_binary64_1397` `distribute-rgt-out--_binary64_1396` `distribute-rgt-out_binary64_1395` `distribute-lft-out--_binary64_1394` `distribute-lft-out_binary64_1393` `count-2_binary64_1390` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `associate-/l_binary64_1387` `associate-/r_binary64_1386` `associate-l_binary64_1383` `associate-r*_binary64_1382` `associate--r-_binary64_1381` `associate--l-_binary64_1380` `associate-+r-_binary64_1376`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	32	15
4	38	15
5	46	15
6	53	15
7	61	15
8	64	15
9	45	15
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 13 to 13 computations (0% saved)

sample45.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms	62×	body	2048	valid
7.0ms	37×	body	1024	valid
6.0ms	131×	body	128	valid
2.0ms	14×	body	512	valid
1.0ms	12×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64_1435`
5×	`+-commutative_binary64_1372`
3×	`sub0-neg_binary64_1429` `associate--r+_binary64_1378` `associate-+l-_binary64_1377` `*-commutative_binary64_1373`
2×	`neg-mul-1_binary64_1438` `--rgt-identity_binary64_1428` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391`
1×	`1-exp_binary64_1486` `neg-sub0_binary64_1437` `associate-l/_binary64_1385` `associate-r/_binary64_1384` `associate--l+_binary64_1379` `associate-+l+_binary64_1375` `associate-+r+_binary64_1374`
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` `unpow3_binary64_1508` `unpow2_binary64_1507` `unpow1/2_binary64_1506` `pow-plus_binary64_1505` `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-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-unmult_binary64_1479` `cube-mult_binary64_1472` `cube-div_binary64_1471` `cube-prod_binary64_1470` `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` `div-sub_binary64_1447` `unsub-neg_binary64_1436` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `-rgt-identity_binary64_1432` `-lft-identity_binary64_1431` `remove-double-neg_binary64_1430` `+-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` `pow-sqr_binary64_1415` `sqr-pow_binary64_1414` `difference-of-sqr--1_binary64_1413` `difference-of-sqr-1_binary64_1412` `difference-of-squares_binary64_1411` `unswap-sqr_binary64_1410` `swap-sqr_binary64_1409` `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-rgt-neg-out_binary64_1402` `distribute-lft-neg-out_binary64_1401` `distribute-rgt-neg-in_binary64_1400` `distribute-lft-neg-in_binary64_1399` `distribute-rgt1-in_binary64_1398` `distribute-lft1-in_binary64_1397` `distribute-rgt-out--_binary64_1396` `distribute-rgt-out_binary64_1395` `distribute-lft-out--_binary64_1394` `distribute-lft-out_binary64_1393` `count-2_binary64_1390` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `associate-/l_binary64_1387` `associate-/r_binary64_1386` `associate-l_binary64_1383` `associate-r*_binary64_1382` `associate--r-_binary64_1381` `associate--l-_binary64_1380` `associate-+r-_binary64_1376`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	32	15
4	38	15
5	46	15
6	53	15
7	61	15
8	64	15
9	45	15

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

17.1b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(hypot.f64 1 x)
0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.6b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite134.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

17.1b

Rules

26×	`*-un-lft-identity_binary64_1442`
24×	`add-sqr-sqrt_binary64_1464`
15×	`add-cube-cbrt_binary64_1477`
12×	`sqrt-prod_binary64_1458`
9×	`times-frac_binary64_1448`
7×	`cancel-sign-sub-inv_binary64_1408`
6×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
5×	`pow1_binary64_1503`
4×	`difference-of-squares_binary64_1411`
3×	`distribute-lft-out_binary64_1393` `distribute-lft-out--_binary64_1394` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`sqrt-div_binary64_1459`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `rem-sqrt-square_binary64_1455`

Counts

4 → 75

Calls

4 calls:

11.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
1.0ms	(hypot.f64 1 x)

Compiler

Compiled 1401 to 1270 computations (9.4% saved)

series242.0ms (2.1%)

Error

17.1b

Counts

4 → 12

Calls

4 calls:

95.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
87.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
40.0ms	(/.f64 1/2 (hypot.f64 1 x))
11.0ms	(hypot.f64 1 x)

Compiler

Compiled 396 to 385 computations (2.8% saved)

simplify133.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

950×	`unsub-neg_binary64_1436`
585×	`times-frac_binary64_1448`
366×	`neg-mul-1_binary64_1438`
355×	`neg-sub0_binary64_1437`
253×	`cancel-sign-sub-inv_binary64_1408`
226×	`distribute-neg-out_binary64_1404`
214×	`distribute-rgt-in_binary64_1392`
189×	`*-commutative_binary64_1373`
182×	`distribute-lft-in_binary64_1391`
179×	`distribute-rgt-neg-out_binary64_1402`
176×	`distribute-lft-neg-out_binary64_1401`
134×	`associate-/l*_binary64_1387`
133×	`distribute-rgt-neg-in_binary64_1400`
129×	`associate-l_binary64_1383`
111×	`div-sub_binary64_1447` `associate-r_binary64_1382`
106×	`distribute-lft-neg-in_binary64_1399`
103×	`sub-neg_binary64_1435`
93×	`associate-/r*_binary64_1386`
87×	`exp-prod_binary64_1494`
82×	`sqr-pow_binary64_1414`
68×	`log-prod_binary64_1528`
66×	`associate-+l+_binary64_1375`
58×	`associate-/l/_binary64_1389`
53×	`associate-*l/_binary64_1385`
52×	`distribute-neg-in_binary64_1403`
51×	`+-commutative_binary64_1372`
50×	`distribute-rgt-out--_binary64_1396`
46×	`unswap-sqr_binary64_1410`
43×	`associate-+r+_binary64_1374`
38×	`associate-/r/_binary64_1388` `associate-*r/_binary64_1384`
36×	`cube-prod_binary64_1470`
32×	`*-lft-identity_binary64_1431` `distribute-rgt-out_binary64_1395`
31×	`rem-sqrt-square_binary64_1455`
30×	`*-rgt-identity_binary64_1432` `associate-+l-_binary64_1377`
29×	`exp-sum_binary64_1488`
28×	`distribute-neg-frac_binary64_1406`
27×	`mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `distribute-rgt1-in_binary64_1398`
24×	`cancel-sign-sub_binary64_1407`
21×	`unpow3_binary64_1508` `sub0-neg_binary64_1429`
18×	`exp-diff_binary64_1490` `pow-sqr_binary64_1415`
17×	`pow-plus_binary64_1505`
16×	`cube-unmult_binary64_1479` `swap-sqr_binary64_1409`
14×	`log-div_binary64_1529` `distribute-lft-out_binary64_1393` `associate--r+_binary64_1378`
13×	`/-rgt-identity_binary64_1433` `difference-of-squares_binary64_1411`
12×	`cube-mult_binary64_1472`
11×	`associate-+r-_binary64_1376`
9×	`cube-div_binary64_1471`
8×	`sqr-neg_binary64_1456` `distribute-lft1-in_binary64_1397`
6×	`+-rgt-identity_binary64_1427` `difference-of-sqr-1_binary64_1412`
5×	`log-pow_binary64_1531` `unpow1/2_binary64_1506` `mul-1-neg_binary64_1434` `--rgt-identity_binary64_1428` `distribute-frac-neg_binary64_1405` `associate--l+_binary64_1379`
4×	`difference-of-sqr--1_binary64_1413`
3×	`exp-neg_binary64_1489` `cube-neg_binary64_1469`
2×	`log-rec_binary64_1530` `rem-square-sqrt_binary64_1454` `div0_binary64_1423` `count-2_binary64_1390`
1×	`unpow2_binary64_1507` `div-exp_binary64_1493` `1-exp_binary64_1486` `exp-1-e_binary64_1485` `rem-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `remove-double-neg_binary64_1430` `+-lft-identity_binary64_1426` `remove-double-div_binary64_1418` `distribute-lft-out--_binary64_1394`
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` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `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` `rec-exp_binary64_1492` `prod-exp_binary64_1491` `e-exp-1_binary64_1487` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `rem-3cbrt-rft_binary64_1468` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `*-inverses_binary64_1422` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `associate--r-_binary64_1381` `associate--l-_binary64_1380`

Counts

87 → 38

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	1374
1	211	1328
2	438	1325
3	1156	1325
4	2275	1307
5	3660	1307
6	4923	1307
7	4821	1307

prune51.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	4	39

Error

16.6b

Counts

39 → 4

Compiler

Compiled 606 to 554 computations (8.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
2.1b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite399.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

16.3b

Rules

95×	`add-sqr-sqrt_binary64_1464`
92×	`*-un-lft-identity_binary64_1442`
71×	`times-frac_binary64_1448`
41×	`add-cube-cbrt_binary64_1477`
28×	`distribute-lft-out_binary64_1393`
16×	`difference-of-squares_binary64_1411`
14×	`sqrt-prod_binary64_1458`
13×	`cancel-sign-sub-inv_binary64_1408`
12×	`associate-/l_binary64_1387` `associate-/r_binary64_1386`
10×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
8×	`distribute-lft-out--_binary64_1394`
6×	`add-log-exp_binary64_1481`
4×	`pow1_binary64_1503` `div-inv_binary64_1439`
3×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
2×	`flip3--_binary64_1446` `flip--_binary64_1417` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `div-sub_binary64_1447` `flip3-+_binary64_1445` `flip-+_binary64_1416`

Counts

4 → 146

Calls

4 calls:

20.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
8.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 4316 to 3882 computations (10.1% saved)

series399.0ms (3.5%)

Error

16.6b

Counts

4 → 12

Calls

4 calls:

219.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
69.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
49.0ms	(/.f64 1/2 (hypot.f64 1 x))
48.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 702 to 655 computations (6.7% saved)

simplify180.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

466×	`div-sub_binary64_1447`
293×	`associate-l_binary64_1383`
262×	`associate-/l*_binary64_1387`
257×	`associate-r_binary64_1382`
237×	`associate-*l/_binary64_1385`
201×	`exp-prod_binary64_1494`
182×	`associate-*r/_binary64_1384`
172×	`distribute-rgt-in_binary64_1392`
170×	`log-prod_binary64_1528`
158×	`distribute-lft-in_binary64_1391`
155×	`log-div_binary64_1529` `sub-neg_binary64_1435`
141×	`associate-/l/_binary64_1389`
133×	`*-commutative_binary64_1373`
115×	`associate-/r*_binary64_1386`
102×	`times-frac_binary64_1448`
96×	`distribute-neg-frac_binary64_1406`
88×	`neg-sub0_binary64_1437`
86×	`exp-diff_binary64_1490`
81×	`neg-mul-1_binary64_1438`
75×	`unsub-neg_binary64_1436`
68×	`associate-/r/_binary64_1388`
62×	`distribute-rgt-neg-in_binary64_1400`
58×	`cancel-sign-sub-inv_binary64_1408`
54×	`cube-prod_binary64_1470`
47×	`+-commutative_binary64_1372`
44×	`distribute-lft-neg-in_binary64_1399` `associate-+l+_binary64_1375`
43×	`associate-+r+_binary64_1374`
42×	`sqr-pow_binary64_1414`
41×	`*-rgt-identity_binary64_1432`
40×	`unswap-sqr_binary64_1410`
39×	`unpow3_binary64_1508`
38×	`*-lft-identity_binary64_1431`
31×	`exp-sum_binary64_1488` `distribute-lft-neg-out_binary64_1401`
24×	`cube-div_binary64_1471`
23×	`distribute-rgt-neg-out_binary64_1402`
22×	`/-rgt-identity_binary64_1433`
18×	`mul0-rgt_binary64_1425` `mul0-lft_binary64_1424`
13×	`log-rec_binary64_1530` `distribute-frac-neg_binary64_1405`
11×	`cube-unmult_binary64_1479` `div0_binary64_1423` `associate-+l-_binary64_1377`
9×	`sub0-neg_binary64_1429` `distribute-neg-in_binary64_1403` `distribute-rgt-out_binary64_1395`
8×	`pow-plus_binary64_1505` `associate--r+_binary64_1378`
6×	`unpow1/2_binary64_1506` `remove-double-neg_binary64_1430` `distribute-rgt1-in_binary64_1398`
5×	`associate-+r-_binary64_1376`
4×	`rem-square-sqrt_binary64_1454` `remove-double-div_binary64_1418` `swap-sqr_binary64_1409` `distribute-lft-out_binary64_1393`
3×	`cube-mult_binary64_1472` `rem-sqrt-square_binary64_1455` `mul-1-neg_binary64_1434` `+-rgt-identity_binary64_1427` `pow-sqr_binary64_1415` `associate--r-_binary64_1381`
2×	`log-pow_binary64_1531` `exp-sqrt_binary64_1495` `rem-3cbrt-lft_binary64_1467`
1×	`div-exp_binary64_1493` `1-exp_binary64_1486` `exp-1-e_binary64_1485` `cube-neg_binary64_1469` `rem-3cbrt-rft_binary64_1468` `sqr-neg_binary64_1456` `*-inverses_binary64_1422` `difference-of-sqr-1_binary64_1412` `distribute-lft1-in_binary64_1397` `associate--l-_binary64_1380`
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` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `unpow2_binary64_1507` `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` `rec-exp_binary64_1492` `prod-exp_binary64_1491` `exp-neg_binary64_1489` `e-exp-1_binary64_1487` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `rem-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `--rgt-identity_binary64_1428` `+-lft-identity_binary64_1426` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `difference-of-sqr--1_binary64_1413` `difference-of-squares_binary64_1411` `cancel-sign-sub_binary64_1407` `distribute-neg-out_binary64_1404` `distribute-rgt-out--_binary64_1396` `distribute-lft-out--_binary64_1394` `count-2_binary64_1390` `associate--l+_binary64_1379`

Counts

158 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	3990
1	426	3855
2	1125	3849
3	3433	3848
4	4361	3848
5	4885	3848

prune133.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	76	4	80

Error

16.3b

Counts

80 → 4

Compiler

Compiled 1839 to 1653 computations (10.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/4 (hypot.f64 1 x))
0.0b	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
0.2b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
2.0b	(-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

rewrite898.0ms (7.8%)

Algorithm

1×	rewrite-expression-head

Error

16.3b

Rules

97×	`add-sqr-sqrt_binary64_1464`
69×	`*-un-lft-identity_binary64_1442`
65×	`times-frac_binary64_1448`
51×	`add-cube-cbrt_binary64_1477`
44×	`unpow-prod-down_binary64_1521` `cube-prod_binary64_1470`
32×	`cancel-sign-sub-inv_binary64_1408`
24×	`difference-of-squares_binary64_1411`
12×	`sqr-pow_binary64_1414`
11×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
7×	`associate-/l*_binary64_1387`
6×	`add-log-exp_binary64_1481` `div-inv_binary64_1439` `associate-/r*_binary64_1386`
5×	`pow1_binary64_1503` `distribute-lft-out--_binary64_1394`
4×	`distribute-lft-out_binary64_1393`
3×	`pow-unpow_binary64_1519` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
2×	`unpow3_binary64_1508` `cube-mult_binary64_1472` `pow-exp_binary64_1510` `rem-cube-cbrt_binary64_1465` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l/_binary64_1389`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `difference-cubes_binary64_1444` `sub-neg_binary64_1435` `flip--_binary64_1417` `pow-pow_binary64_1514` `pow-to-exp_binary64_1511` `cube-div_binary64_1471` `flip3-+_binary64_1445` `flip-+_binary64_1416`

Counts

4 → 179

Calls

4 calls:

28.0ms	(-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
9.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
3.0ms	(/.f64 1/4 (hypot.f64 1 x))

Compiler

Compiled 8438 to 7551 computations (10.5% saved)

series455.0ms (4%)

Error

16.3b

Counts

4 → 12

Calls

4 calls:

154.0ms	(-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
110.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
108.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
54.0ms	(/.f64 1/4 (hypot.f64 1 x))

Compiler

Compiled 1314 to 1195 computations (9.1% saved)

simplify166.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

754×	`times-frac_binary64_1448`
491×	`log-prod_binary64_1528`
411×	`unswap-sqr_binary64_1410`
187×	`associate-r_binary64_1382`
165×	`associate-l_binary64_1383`
157×	`exp-prod_binary64_1494`
113×	`sqr-pow_binary64_1414`
110×	`log-div_binary64_1529`
99×	`cube-prod_binary64_1470`
95×	`associate-*l/_binary64_1385`
89×	`associate-*r/_binary64_1384`
83×	`cube-div_binary64_1471`
76×	`cancel-sign-sub-inv_binary64_1408`
74×	`neg-mul-1_binary64_1438`
71×	`neg-sub0_binary64_1437`
68×	`sub-neg_binary64_1435`
64×	`*-commutative_binary64_1373`
60×	`associate-/l*_binary64_1387`
56×	`distribute-rgt-neg-in_binary64_1400`
47×	`+-commutative_binary64_1372`
46×	`distribute-lft-neg-in_binary64_1399`
42×	`log-pow_binary64_1531`
41×	`associate-/l/_binary64_1389`
37×	`unpow3_binary64_1508`
35×	`cube-mult_binary64_1472`
30×	`associate-/r*_binary64_1386`
28×	`distribute-rgt-in_binary64_1392`
22×	`distribute-lft-in_binary64_1391`
19×	`pow-sqr_binary64_1415`
18×	`distribute-lft-neg-out_binary64_1401`
14×	`rem-sqrt-square_binary64_1455` `distribute-neg-frac_binary64_1406`
13×	`*-rgt-identity_binary64_1432` `associate-/r/_binary64_1388` `associate-+r-_binary64_1376`
12×	`difference-of-squares_binary64_1411`
11×	`pow-plus_binary64_1505` `*-lft-identity_binary64_1431`
10×	`cube-unmult_binary64_1479` `swap-sqr_binary64_1409`
9×	`/-rgt-identity_binary64_1433`
7×	`distribute-rgt-neg-out_binary64_1402`
6×	`div-sub_binary64_1447`
5×	`associate-+l+_binary64_1375`
4×	`log-rec_binary64_1530` `exp-sum_binary64_1488` `rem-square-sqrt_binary64_1454` `unsub-neg_binary64_1436` `distribute-rgt-out_binary64_1395` `associate-+r+_binary64_1374`
3×	`rem-cube-cbrt_binary64_1465` `+-rgt-identity_binary64_1427` `distribute-neg-in_binary64_1403`
2×	`unpow1/2_binary64_1506` `rem-cbrt-cube_binary64_1466` `mul-1-neg_binary64_1434` `distribute-rgt1-in_binary64_1398` `associate--r+_binary64_1378`
1×	`unpow1_binary64_1500` `div-exp_binary64_1493` `exp-diff_binary64_1490` `1-exp_binary64_1486` `distribute-rgt-out--_binary64_1396` `associate-+l-_binary64_1377`
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` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `unpow2_binary64_1507` `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` `rec-exp_binary64_1492` `prod-exp_binary64_1491` `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-neg_binary64_1469` `rem-3cbrt-rft_binary64_1468` `rem-3cbrt-lft_binary64_1467` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `remove-double-neg_binary64_1430` `sub0-neg_binary64_1429` `--rgt-identity_binary64_1428` `+-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-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-lft1-in_binary64_1397` `distribute-lft-out--_binary64_1394` `distribute-lft-out_binary64_1393` `count-2_binary64_1390` `associate--r-_binary64_1381` `associate--l-_binary64_1380` `associate--l+_binary64_1379`

Counts

191 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	4101
1	614	3734
2	2258	3608
3	4846	3608
4	5472	3608

prune476.0ms (4.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	0	2	2
Picked	1	0	1
Done	1	0	1
Total	133	5	138

Error

16.3b

Counts

138 → 5

Compiler

Compiled 5760 to 5150 computations (10.6% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x)))) (hypot.f64 1 x))
0.2b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
0.5b	(*.f64 (sqrt.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x)))) (/.f64 (sqrt.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x)))) (hypot.f64 1 x)))
2.0b	(-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

rewrite1.5s (13.2%)

Algorithm

1×	rewrite-expression-head

Error

16.3b

Rules

128×	`add-sqr-sqrt_binary64_1464`
92×	`*-un-lft-identity_binary64_1442`
90×	`times-frac_binary64_1448`
66×	`add-cube-cbrt_binary64_1477`
44×	`unpow-prod-down_binary64_1521` `cube-prod_binary64_1470`
37×	`sqrt-prod_binary64_1458`
32×	`cancel-sign-sub-inv_binary64_1408`
25×	`associate-r_binary64_1382`
24×	`difference-of-squares_binary64_1411`
14×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
12×	`sqr-pow_binary64_1414`
8×	`distribute-lft-out_binary64_1393`
7×	`pow1_binary64_1503` `associate-l_binary64_1383` `associate-/l*_binary64_1387`
6×	`add-log-exp_binary64_1481` `div-inv_binary64_1439` `sqrt-div_binary64_1459` `unswap-sqr_binary64_1410`
5×	`distribute-lft-out--_binary64_1394`
3×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-unpow_binary64_1519` `associate-/r*_binary64_1386`
2×	`unpow3_binary64_1508` `cube-mult_binary64_1472` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `frac-times_binary64_1452` `associate-*l/_binary64_1385` `pow-exp_binary64_1510` `rem-cube-cbrt_binary64_1465` `associate-/l/_binary64_1389`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `difference-cubes_binary64_1444` `sub-neg_binary64_1435` `flip--_binary64_1417` `pow-prod-down_binary64_1513` `associate-r/_binary64_1384` `-commutative_binary64_1373` `pow-pow_binary64_1514` `pow-to-exp_binary64_1511` `cube-div_binary64_1471` `frac-2neg_binary64_1453` `clear-num_binary64_1441`

Counts

4 → 220

Calls

4 calls:

28.0ms	(-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
25.0ms	(*.f64 (sqrt.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x)))) (/.f64 (sqrt.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x)))) (hypot.f64 1 x)))
14.0ms	(/.f64 (sqrt.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x)))) (hypot.f64 1 x))
6.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

Compiler

Compiled 13082 to 11703 computations (10.5% saved)

series560.0ms (4.9%)

Error

16.3b

Counts

4 → 12

Calls

4 calls:

150.0ms	(/.f64 (sqrt.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x)))) (hypot.f64 1 x))
143.0ms	(-.f64 (pow.f64 1/2 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
126.0ms	(*.f64 (sqrt.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x)))) (/.f64 (sqrt.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x)))) (hypot.f64 1 x)))
107.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

Compiler

Compiled 1620 to 1474 computations (9% saved)

simplify215.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

476×	`unswap-sqr_binary64_1410`
352×	`log-prod_binary64_1528`
339×	`cancel-sign-sub-inv_binary64_1408`
261×	`associate-r_binary64_1382`
239×	`associate-l_binary64_1383`
160×	`exp-prod_binary64_1494`
127×	`log-div_binary64_1529`
125×	`associate-*r/_binary64_1384`
121×	`associate-*l/_binary64_1385`
119×	`sqr-pow_binary64_1414`
112×	`cube-prod_binary64_1470`
92×	`associate-/l*_binary64_1387`
90×	`*-commutative_binary64_1373`
89×	`cube-div_binary64_1471`
79×	`swap-sqr_binary64_1409`
75×	`neg-mul-1_binary64_1438`
73×	`neg-sub0_binary64_1437` `sub-neg_binary64_1435`
59×	`distribute-rgt-neg-in_binary64_1400`
52×	`+-commutative_binary64_1372`
47×	`distribute-lft-neg-in_binary64_1399`
44×	`associate-/l/_binary64_1389`
42×	`log-pow_binary64_1531`
38×	`unpow3_binary64_1508`
37×	`times-frac_binary64_1448`
36×	`cube-mult_binary64_1472` `associate-/r*_binary64_1386`
31×	`*-rgt-identity_binary64_1432`
25×	`*-lft-identity_binary64_1431`
21×	`pow-sqr_binary64_1415`
19×	`distribute-lft-neg-out_binary64_1401`
17×	`rem-sqrt-square_binary64_1455`
15×	`/-rgt-identity_binary64_1433` `distribute-neg-frac_binary64_1406`
14×	`associate-+r-_binary64_1376`
12×	`pow-plus_binary64_1505` `cube-unmult_binary64_1479` `difference-of-squares_binary64_1411`
10×	`associate-/r/_binary64_1388`
7×	`log-rec_binary64_1530` `distribute-rgt-neg-out_binary64_1402`
6×	`rem-square-sqrt_binary64_1454` `associate-+l+_binary64_1375`
5×	`div-sub_binary64_1447` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391`
4×	`exp-sum_binary64_1488` `distribute-rgt-out_binary64_1395` `associate-+r+_binary64_1374`
3×	`rem-cube-cbrt_binary64_1465` `unsub-neg_binary64_1436` `+-rgt-identity_binary64_1427`
2×	`rem-cbrt-cube_binary64_1466` `distribute-rgt1-in_binary64_1398` `associate-+l-_binary64_1377`
1×	`unpow1/2_binary64_1506` `unpow1_binary64_1500` `div-exp_binary64_1493` `exp-diff_binary64_1490` `1-exp_binary64_1486` `exp-1-e_binary64_1485` `mul-1-neg_binary64_1434` `distribute-rgt-out--_binary64_1396` `count-2_binary64_1390`
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` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `unpow2_binary64_1507` `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` `rec-exp_binary64_1492` `prod-exp_binary64_1491` `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` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `remove-double-neg_binary64_1430` `sub0-neg_binary64_1429` `--rgt-identity_binary64_1428` `+-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-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-neg-in_binary64_1403` `distribute-lft1-in_binary64_1397` `distribute-lft-out--_binary64_1394` `distribute-lft-out_binary64_1393` `associate--r-_binary64_1381` `associate--l-_binary64_1380` `associate--l+_binary64_1379` `associate--r+_binary64_1378`

Counts

232 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	6217
1	686	5553
2	2640	5395
3	4655	5395
4	5022	5395

prune951.0ms (8.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	183	5	188

Error

16.3b

Counts

188 → 5

Compiler

Compiled 9518 to 8499 computations (10.7% saved)

regimes1.0s (9%)

Accuracy

Total 0.3b remaining (2%)

Threshold costs 0.3b (2%)

Compiler

Compiled 13485 to 12463 computations (7.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64_1372`
2×	`sub-neg_binary64_1435` `*-commutative_binary64_1373`
1×	`1-exp_binary64_1486` `neg-mul-1_binary64_1438` `neg-sub0_binary64_1437`
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` `unsub-neg_binary64_1436` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `-rgt-identity_binary64_1432` `-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-rgt-neg-out_binary64_1402` `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	21	51
1	30	51
2	34	51
3	36	51
4	37	51
5	35	51

end0.0ms (0%)

sample3.2s (28.2%)

Algorithm

1×

intervals

Results

556.0ms	2049×	body	2048	valid
196.0ms	976×	body	1024	valid
195.0ms	4229×	body	128	valid
68.0ms	485×	body	512	valid
26.0ms	261×	body	256	valid

Compiler

Compiled 1960 to 1812 computations (7.6% saved)

Details

analyze146.0ms (1.3%)

sample45.0ms (0.4%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

rewrite134.0ms (1.2%)

series242.0ms (2.1%)

simplify133.0ms (1.2%)

prune51.0ms (0.5%)

localize11.0ms (0.1%)

rewrite399.0ms (3.5%)

series399.0ms (3.5%)

simplify180.0ms (1.6%)

prune133.0ms (1.2%)

localize24.0ms (0.2%)

rewrite898.0ms (7.8%)

series455.0ms (4%)

simplify166.0ms (1.4%)

prune476.0ms (4.2%)

localize27.0ms (0.2%)

rewrite1.5s (13.2%)

series560.0ms (4.9%)

simplify215.0ms (1.9%)

prune951.0ms (8.3%)

regimes1.0s (9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.2s (28.2%)

Profiling