Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 6 to 6 computations (0% saved)

sample18.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 11 to 13 computations (-18.2% saved)

simplify949.0ms (15.8%)

Algorithm

1×	egg-herbie

Rules

1217×	`exp-prod_binary64_1494`
711×	`swap-sqr_binary64_1409`
551×	`distribute-rgt-out--_binary64_1396`
523×	`distribute-rgt-out_binary64_1395`
496×	`cube-prod_binary64_1470`
419×	`sub-neg_binary64_1435`
319×	`distribute-rgt-neg-in_binary64_1400`
291×	`unsub-neg_binary64_1436`
276×	`div-sub_binary64_1447`
255×	`exp-sum_binary64_1488`
245×	`exp-diff_binary64_1490`
179×	`associate--r-_binary64_1381`
172×	`*-commutative_binary64_1373`
170×	`cancel-sign-sub-inv_binary64_1408`
161×	`sqr-pow_binary64_1414`
137×	`neg-mul-1_binary64_1438`
132×	`neg-sub0_binary64_1437`
120×	`associate--l-_binary64_1380`
118×	`pow-plus_binary64_1505`
117×	`pow-sqr_binary64_1415`
113×	`associate-+r-_binary64_1376`
73×	`associate-+l-_binary64_1377` `+-commutative_binary64_1372`
49×	`distribute-lft-neg-in_binary64_1399`
47×	`distribute-neg-out_binary64_1404`
46×	`distribute-rgt1-in_binary64_1398`
37×	`distribute-rgt-in_binary64_1392`
21×	`distribute-neg-in_binary64_1403`
19×	`associate-r_binary64_1382`
17×	`associate--r+_binary64_1378`
16×	`distribute-lft-in_binary64_1391` `associate-+l+_binary64_1375`
15×	`sqr-neg_binary64_1456` `+-inverses_binary64_1421` `difference-of-squares_binary64_1411`
14×	`pow-base-1_binary64_1502` `associate-+r+_binary64_1374`
13×	`remove-double-neg_binary64_1430` `count-2_binary64_1390`
11×	`cube-unmult_binary64_1479` `distribute-lft1-in_binary64_1397`
10×	`exp-lft-sqr_binary64_1497` `associate--l+_binary64_1379`
9×	`distribute-rgt-neg-out_binary64_1402`
8×	`*-rgt-identity_binary64_1432` `distribute-lft-neg-out_binary64_1401`
6×	`*-lft-identity_binary64_1431`
5×	`sub0-neg_binary64_1429` `--rgt-identity_binary64_1428` `+-rgt-identity_binary64_1427` `difference-of-sqr--1_binary64_1413` `associate-l/_binary64_1385` `associate-l*_binary64_1383`
4×	`+-lft-identity_binary64_1426`
3×	`distribute-lft-out--_binary64_1394` `distribute-lft-out_binary64_1393`
2×	`exp-neg_binary64_1489` `cube-div_binary64_1471` `mul0-lft_binary64_1424`
1×	`unpow3_binary64_1508` `1-exp_binary64_1486` `exp-1-e_binary64_1485` `cube-neg_binary64_1469` `div0_binary64_1423` `*-inverses_binary64_1422` `distribute-neg-frac_binary64_1406`
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` `unpow2_binary64_1507` `unpow1/2_binary64_1506` `exp-to-pow_binary64_1504` `unpow0_binary64_1501` `unpow1_binary64_1500` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `div-exp_binary64_1493` `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` `cube-mult_binary64_1472` `rem-3cbrt-rft_binary64_1468` `rem-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `rem-sqrt-square_binary64_1455` `rem-square-sqrt_binary64_1454` `times-frac_binary64_1448` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `mul0-rgt_binary64_1425` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `remove-double-div_binary64_1418` `difference-of-sqr-1_binary64_1412` `unswap-sqr_binary64_1410` `cancel-sign-sub_binary64_1407` `distribute-frac-neg_binary64_1405` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `associate-/l_binary64_1387` `associate-/r_binary64_1386` `associate-*r/_binary64_1384`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	13	8
3	19	8
4	27	8
5	42	8
6	88	8
7	202	8
8	1788	8
9	2281	8

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

1 → 1

Compiler

Compiled 5 to 5 computations (0% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

3×	`add-sqr-sqrt_binary64_1464` `sqrt-prod_binary64_1458`
2×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
1×	`pow1/2_binary64_1522` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455`

Counts

1 → 13

Calls

1 calls:

1.0ms

(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 139 to 36 computations (74.1% saved)

series77.0ms (1.3%)

Error

0.0b

Counts

1 → 6

Calls

1 calls:

74.0ms

(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 90 to 65 computations (27.8% saved)

simplify752.0ms (12.5%)

Algorithm

1×	egg-herbie

Rules

1232×	`exp-prod_binary64_1494`
522×	`cube-prod_binary64_1470`
506×	`distribute-rgt-out--_binary64_1396`
478×	`distribute-rgt-out_binary64_1395`
359×	`associate-/r*_binary64_1386`
304×	`swap-sqr_binary64_1409`
294×	`exp-diff_binary64_1490`
268×	`distribute-rgt-neg-in_binary64_1400`
252×	`exp-sum_binary64_1488` `sub-neg_binary64_1435`
216×	`unswap-sqr_binary64_1410`
213×	`*-commutative_binary64_1373`
166×	`unsub-neg_binary64_1436`
163×	`cancel-sign-sub-inv_binary64_1408`
155×	`div-sub_binary64_1447`
152×	`associate-/r/_binary64_1388`
142×	`associate--r-_binary64_1381`
141×	`pow-plus_binary64_1505`
116×	`associate--l-_binary64_1380`
113×	`associate-+r-_binary64_1376`
76×	`associate-/l*_binary64_1387`
74×	`+-commutative_binary64_1372`
73×	`associate-+l-_binary64_1377`
46×	`distribute-lft-neg-in_binary64_1399`
45×	`cube-div_binary64_1471` `sqr-pow_binary64_1414`
43×	`distribute-neg-out_binary64_1404`
42×	`distribute-rgt1-in_binary64_1398`
35×	`distribute-rgt-in_binary64_1392`
33×	`neg-mul-1_binary64_1438` `associate-/l/_binary64_1389`
32×	`associate-r_binary64_1382`
31×	`neg-sub0_binary64_1437`
29×	`associate-l_binary64_1383`
27×	`pow-sqr_binary64_1415`
25×	`distribute-frac-neg_binary64_1405`
23×	`difference-of-squares_binary64_1411`
20×	`distribute-lft-neg-out_binary64_1401`
18×	`cube-unmult_binary64_1479` `distribute-rgt-neg-out_binary64_1402`
17×	`distribute-neg-in_binary64_1403` `associate--r+_binary64_1378`
15×	`associate-*r/_binary64_1384` `associate-+l+_binary64_1375`
14×	`times-frac_binary64_1448` `associate-+r+_binary64_1374`
13×	`pow-base-1_binary64_1502` `exp-lft-sqr_binary64_1497` `+-inverses_binary64_1421`
12×	`distribute-lft1-in_binary64_1397` `distribute-lft-in_binary64_1391` `count-2_binary64_1390`
10×	`associate--l+_binary64_1379`
9×	`remove-double-neg_binary64_1430` `distribute-neg-frac_binary64_1406`
7×	`exp-sqrt_binary64_1495`
5×	`unpow3_binary64_1508` `-rgt-identity_binary64_1432` `-lft-identity_binary64_1431`
4×	`exp-neg_binary64_1489` `cube-mult_binary64_1472` `rem-sqrt-square_binary64_1455` `sub0-neg_binary64_1429` `+-rgt-identity_binary64_1427` `+-lft-identity_binary64_1426`
3×	`/-rgt-identity_binary64_1433` `difference-of-sqr--1_binary64_1413` `distribute-lft-out--_binary64_1394` `distribute-lft-out_binary64_1393` `associate-*l/_binary64_1385`
2×	`sqr-neg_binary64_1456` `--rgt-identity_binary64_1428` `mul0-lft_binary64_1424`
1×	`1-exp_binary64_1486` `exp-1-e_binary64_1485` `cube-neg_binary64_1469` `rem-square-sqrt_binary64_1454` `div0_binary64_1423` `*-inverses_binary64_1422` `remove-double-div_binary64_1418`
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` `unpow2_binary64_1507` `unpow1/2_binary64_1506` `exp-to-pow_binary64_1504` `unpow0_binary64_1501` `unpow1_binary64_1500` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-cbrt_binary64_1496` `div-exp_binary64_1493` `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-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `mul-1-neg_binary64_1434` `mul0-rgt_binary64_1425` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `difference-of-sqr-1_binary64_1412` `cancel-sign-sub_binary64_1407`

Counts

19 → 4

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	21	191
1	27	186
2	34	186
3	43	186
4	56	186
5	87	186
6	169	186
7	385	186
8	2127	184
9	3422	184

prune5.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

0.0b

Counts

5 → 2

Compiler

Compiled 52 to 24 computations (53.8% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (cbrt.f64 (fabs.f64 (-.f64 x y))))
0.3b	(*.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))
0.6b	(cbrt.f64 (fabs.f64 (-.f64 x y)))
0.6b	(cbrt.f64 (fabs.f64 (-.f64 x y)))

rewrite81.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

20×	`add-sqr-sqrt_binary64_1464`
14×	`cbrt-prod_binary64_1473` `sqrt-prod_binary64_1458`
12×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`associate-r_binary64_1382`
7×	`pow1_binary64_1503`
6×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
4×	`add-log-exp_binary64_1481`
3×	`pow1/3_binary64_1524` `unswap-sqr_binary64_1410` `associate-l_binary64_1383`
2×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455`
1×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `*-commutative_binary64_1373` `pow1/2_binary64_1522`

Counts

4 → 66

Calls

4 calls:

7.0ms	(*.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))
2.0ms	(sqrt.f64 (cbrt.f64 (fabs.f64 (-.f64 x y))))
1.0ms	(cbrt.f64 (fabs.f64 (-.f64 x y)))
1.0ms	(cbrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 1395 to 205 computations (85.3% saved)

series1.3s (21.4%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

381.0ms	(*.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))
313.0ms	(sqrt.f64 (cbrt.f64 (fabs.f64 (-.f64 x y))))
293.0ms	(cbrt.f64 (fabs.f64 (-.f64 x y)))
282.0ms	(cbrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 990 to 577 computations (41.7% saved)

simplify504.0ms (8.4%)

Algorithm

1×	egg-herbie

Rules

771×	`distribute-rgt-in_binary64_1392`
749×	`distribute-lft-in_binary64_1391`
473×	`log-prod_binary64_1528`
364×	`times-frac_binary64_1448`
349×	`associate-/l*_binary64_1387`
325×	`distribute-rgt-out--_binary64_1396`
290×	`sqr-pow_binary64_1414`
256×	`associate-l_binary64_1383`
220×	`associate-/l/_binary64_1389`
194×	`unswap-sqr_binary64_1410`
193×	`log-pow_binary64_1531`
192×	`pow-sqr_binary64_1415`
181×	`*-commutative_binary64_1373`
166×	`associate-r_binary64_1382`
115×	`count-2_binary64_1390`
110×	`associate-/r/_binary64_1388`
107×	`cancel-sign-sub-inv_binary64_1408`
99×	`exp-prod_binary64_1494`
79×	`associate-*r/_binary64_1384`
74×	`distribute-rgt-out_binary64_1395` `associate-/r*_binary64_1386`
72×	`associate-*l/_binary64_1385`
66×	`log-div_binary64_1529`
62×	`distribute-rgt1-in_binary64_1398`
55×	`cube-prod_binary64_1470`
53×	`distribute-lft-neg-in_binary64_1399`
49×	`distribute-neg-frac_binary64_1406`
46×	`pow-plus_binary64_1505`
45×	`*-rgt-identity_binary64_1432`
44×	`distribute-rgt-neg-in_binary64_1400`
35×	`*-lft-identity_binary64_1431`
30×	`distribute-lft-out_binary64_1393`
27×	`associate-+l-_binary64_1377`
26×	`associate-+r-_binary64_1376`
22×	`rem-sqrt-square_binary64_1455`
21×	`/-rgt-identity_binary64_1433` `distribute-lft-out--_binary64_1394`
19×	`swap-sqr_binary64_1409`
18×	`sub-neg_binary64_1435`
17×	`distribute-lft1-in_binary64_1397`
16×	`cube-div_binary64_1471` `associate--r+_binary64_1378`
13×	`exp-sqrt_binary64_1495` `cube-unmult_binary64_1479` `div-sub_binary64_1447` `neg-mul-1_binary64_1438`
12×	`neg-sub0_binary64_1437`
10×	`log-rec_binary64_1530` `exp-to-pow_binary64_1504` `distribute-neg-in_binary64_1403` `associate--l+_binary64_1379`
9×	`+-commutative_binary64_1372`
8×	`unpow3_binary64_1508` `exp-lft-sqr_binary64_1497` `mul0-lft_binary64_1424`
7×	`cube-mult_binary64_1472` `associate-+r+_binary64_1374`
6×	`unsub-neg_binary64_1436` `associate--r-_binary64_1381`
5×	`mul0-rgt_binary64_1425` `associate--l-_binary64_1380`
4×	`pow-base-1_binary64_1502` `associate-+l+_binary64_1375`
3×	`exp-sum_binary64_1488` `sub0-neg_binary64_1429` `--rgt-identity_binary64_1428` `*-inverses_binary64_1422` `remove-double-div_binary64_1418`
2×	`prod-exp_binary64_1491` `rem-log-exp_binary64_1483` `remove-double-neg_binary64_1430`
1×	`unpow1/3_binary64_1509` `exp-lft-cube_binary64_1498` `div-exp_binary64_1493` `exp-diff_binary64_1490` `1-exp_binary64_1486` `exp-1-e_binary64_1485` `rem-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `sqr-abs_binary64_1457` `rem-square-sqrt_binary64_1454` `+-rgt-identity_binary64_1427` `rgt-mult-inverse_binary64_1419` `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` `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` `unpow2_binary64_1507` `unpow1/2_binary64_1506` `unpow0_binary64_1501` `unpow1_binary64_1500` `unpow-1_binary64_1499` `exp-cbrt_binary64_1496` `rec-exp_binary64_1492` `exp-neg_binary64_1489` `e-exp-1_binary64_1487` `exp-0_binary64_1484` `rem-exp-log_binary64_1482` `cube-neg_binary64_1469` `rem-3cbrt-rft_binary64_1468` `rem-cube-cbrt_binary64_1465` `sqr-neg_binary64_1456` `mul-1-neg_binary64_1434` `+-lft-identity_binary64_1426` `div0_binary64_1423` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `difference-of-sqr--1_binary64_1413` `difference-of-sqr-1_binary64_1412` `difference-of-squares_binary64_1411` `cancel-sign-sub_binary64_1407` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-lft-neg-out_binary64_1401`

Counts

90 → 61

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	68	1521
1	111	1480
2	308	1480
3	686	1480
4	1231	1466
5	3286	1451
6	3147	1425
7	4826	1425

prune54.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	60	3	63

Error

Counts

63 → 3

Compiler

Compiled 1074 to 221 computations (79.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (fabs.f64 (-.f64 x y)))
0.6b	(cbrt.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))
0.6b	(cbrt.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))
0.6b	(cbrt.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))

rewrite71.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`cbrt-prod_binary64_1473`
8×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
4×	`pow1/3_binary64_1524` `pow1_binary64_1503` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))
1.0ms	(cbrt.f64 (fabs.f64 (-.f64 x y)))
1.0ms	(cbrt.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))
1.0ms	(cbrt.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))

Compiler

Compiled 1648 to 188 computations (88.6% saved)

series1.4s (23.8%)

Error

Counts

4 → 24

Calls

4 calls:

367.0ms	(cbrt.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))
364.0ms	(cbrt.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))
361.0ms	(cbrt.f64 (fabs.f64 (cbrt.f64 (fabs.f64 (-.f64 x y)))))
302.0ms	(cbrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 2286 to 928 computations (59.4% saved)

simplify116.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

780×	`distribute-rgt-in_binary64_1392`
768×	`distribute-lft-in_binary64_1391`
448×	`unswap-sqr_binary64_1410`
284×	`associate-+l+_binary64_1375`
274×	`associate-+r+_binary64_1374`
222×	`log-prod_binary64_1528`
140×	`distribute-rgt-out_binary64_1395`
137×	`associate-l_binary64_1383`
81×	`associate-*l/_binary64_1385`
71×	`associate-*r/_binary64_1384`
66×	`sqr-pow_binary64_1414`
62×	`associate-r_binary64_1382`
55×	`distribute-lft-out_binary64_1393`
48×	`associate-/l*_binary64_1387`
40×	`pow-sqr_binary64_1415`
36×	`exp-prod_binary64_1494`
34×	`log-pow_binary64_1531`
28×	`count-2_binary64_1390`
24×	`cube-prod_binary64_1470`
23×	`associate-/l/_binary64_1389`
14×	`distribute-rgt1-in_binary64_1398` `*-commutative_binary64_1373`
10×	`rem-sqrt-square_binary64_1455`
9×	`cube-unmult_binary64_1479`
8×	`pow-plus_binary64_1505`
5×	`sub-neg_binary64_1435`
4×	`associate-/r/_binary64_1388`
3×	`neg-mul-1_binary64_1438` `distribute-neg-in_binary64_1403` `associate--r+_binary64_1378` `+-commutative_binary64_1372`
2×	`unpow1/3_binary64_1509` `unpow3_binary64_1508` `rem-3cbrt-lft_binary64_1467` `times-frac_binary64_1448` `neg-sub0_binary64_1437` `+-rgt-identity_binary64_1427` `associate-/r*_binary64_1386` `associate-+l-_binary64_1377` `associate-+r-_binary64_1376`
1×	`1-exp_binary64_1486` `sub0-neg_binary64_1429` `*-inverses_binary64_1422`
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` `unpow2_binary64_1507` `unpow1/2_binary64_1506` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow1_binary64_1500` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `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-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `rem-square-sqrt_binary64_1454` `div-sub_binary64_1447` `unsub-neg_binary64_1436` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `-rgt-identity_binary64_1432` `-lft-identity_binary64_1431` `remove-double-neg_binary64_1430` `--rgt-identity_binary64_1428` `+-lft-identity_binary64_1426` `mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `div0_binary64_1423` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `remove-double-div_binary64_1418` `difference-of-sqr--1_binary64_1413` `difference-of-sqr-1_binary64_1412` `difference-of-squares_binary64_1411` `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-rgt-neg-out_binary64_1402` `distribute-lft-neg-out_binary64_1401` `distribute-rgt-neg-in_binary64_1400` `distribute-lft-neg-in_binary64_1399` `distribute-lft1-in_binary64_1397` `distribute-rgt-out--_binary64_1396` `distribute-lft-out--_binary64_1394` `associate--r-_binary64_1381` `associate--l-_binary64_1380` `associate--l+_binary64_1379`

Counts

68 → 36

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	988
1	45	952
2	97	952
3	223	952
4	747	952

prune47.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	36	3	39

Error

Counts

39 → 3

Compiler

Compiled 1180 to 81 computations (93.1% saved)

regimes78.0ms (1.3%)

Accuracy

Total 0.0b remaining (50%)

Threshold costs 0.0b (50%)

Compiler

Compiled 568 to 287 computations (49.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`sub-neg_binary64_1435` `+-commutative_binary64_1372`
1×	`neg-mul-1_binary64_1438` `neg-sub0_binary64_1437` `*-commutative_binary64_1373`
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` `1-exp_binary64_1486` `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	6	8
1	8	8
2	13	8
3	15	8
4	16	8

Proof

(sqrt f64 (fabs f64 (- f64 h0 h1)))

end0.0ms (0%)

sample493.0ms (8.2%)

Algorithm

1×

intervals

Results

178.0ms

8000×

body

128

valid

Compiler

Compiled 119 to 64 computations (46.2% saved)

Details

analyze2.0ms (0%)

sample18.0ms (0.3%)

simplify949.0ms (15.8%)

prune1.0ms (0%)

localize4.0ms (0.1%)

rewrite11.0ms (0.2%)

series77.0ms (1.3%)

simplify752.0ms (12.5%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

rewrite81.0ms (1.4%)

series1.3s (21.4%)

simplify504.0ms (8.4%)

prune54.0ms (0.9%)

localize14.0ms (0.2%)

rewrite71.0ms (1.2%)

series1.4s (23.8%)

simplify116.0ms (1.9%)

prune47.0ms (0.8%)

regimes78.0ms (1.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample493.0ms (8.2%)

Profiling