Details

analyze3.6s (15.2%)

Algorithm

1×	search
2×	egg-herbie

Rules

501×	`unsub-neg_binary64_1436`
469×	`distribute-rgt-in_binary64_1392`
417×	`distribute-rgt-neg-in_binary64_1400`
332×	`distribute-lft-in_binary64_1391`
290×	`cancel-sign-sub-inv_binary64_1408`
267×	`distribute-lft-neg-in_binary64_1399`
266×	`neg-mul-1_binary64_1438`
265×	`neg-sub0_binary64_1437`
247×	`distribute-lft-neg-out_binary64_1401`
229×	`associate--r+_binary64_1378`
192×	`sub-neg_binary64_1435`
189×	`distribute-neg-in_binary64_1403`
168×	`*-commutative_binary64_1373`
153×	`distribute-rgt-neg-out_binary64_1402`
142×	`associate-r_binary64_1382`
140×	`associate-l_binary64_1383`
113×	`mul0-rgt_binary64_1425` `mul0-lft_binary64_1424`
102×	`+-commutative_binary64_1372`
93×	`remove-double-neg_binary64_1430`
47×	`*-lft-identity_binary64_1431`
46×	`*-rgt-identity_binary64_1432`
38×	`associate-+l-_binary64_1377`
35×	`associate--r-_binary64_1381`
31×	`sub0-neg_binary64_1429`
24×	`associate--l+_binary64_1379`
23×	`associate-+r+_binary64_1374`
17×	`associate-+r-_binary64_1376`
15×	`associate-+l+_binary64_1375`
14×	`cos-neg_binary64_1573` `mul-1-neg_binary64_1434` `+-rgt-identity_binary64_1427`
12×	`sin-neg_binary64_1572` `distribute-rgt-out--_binary64_1396` `associate--l-_binary64_1380`
8×	`cancel-sign-sub_binary64_1407`
5×	`+-lft-identity_binary64_1426` `distribute-lft-out--_binary64_1394`
3×	`distribute-neg-out_binary64_1404`
1×	`1-exp_binary64_1486` `swap-lambda1-lambda2` `swap-phi1-phi2`
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` `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` `/-rgt-identity_binary64_1433` `--rgt-identity_binary64_1428` `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` `distribute-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-rgt1-in_binary64_1398` `distribute-lft1-in_binary64_1397` `distribute-rgt-out_binary64_1395` `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_1385` `associate-*r/_binary64_1384`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	341
1	164	341
2	237	341
3	274	341
4	306	341
5	447	341
6	475	341
7	707	341
8	1046	341
9	1135	341
10	1279	341
11	1600	341
12	1905	341
13	2500	341
14	2503	341
15	2479	341
16	2493	341
17	2493	341
18	2893	341
19	2619	341
20	2619	341
21	2619	341
22	2619	341
23	2392	341
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 20 to 18 computations (10% saved)

sample224.0ms (0.9%)

Algorithm

1×

intervals

Results

132.0ms	166×	body	1024	valid
25.0ms	49×	body	512	valid
20.0ms	10×	body	2048	valid
14.0ms	22×	body	256	valid
1.0ms	9×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64_1435`
14×	`cancel-sign-sub-inv_binary64_1408`
10×	`distribute-rgt-in_binary64_1392` `*-commutative_binary64_1373`
9×	`neg-mul-1_binary64_1438`
8×	`associate--r+_binary64_1378`
7×	`unsub-neg_binary64_1436`
6×	`neg-sub0_binary64_1437` `associate--r-_binary64_1381`
5×	`distribute-neg-in_binary64_1403` `distribute-lft-neg-out_binary64_1401` `distribute-rgt-neg-in_binary64_1400` `distribute-lft-in_binary64_1391` `+-commutative_binary64_1372`
4×	`*-lft-identity_binary64_1431` `sub0-neg_binary64_1429` `associate-+l-_binary64_1377`
3×	`+-lft-identity_binary64_1426` `distribute-rgt-neg-out_binary64_1402` `associate-l_binary64_1383` `associate-r_binary64_1382` `associate-+l+_binary64_1375`
2×	`cos-neg_binary64_1573` `*-rgt-identity_binary64_1432`
1×	`1-exp_binary64_1486` `remove-double-neg_binary64_1430` `--rgt-identity_binary64_1428` `+-rgt-identity_binary64_1427` `distribute-lft-neg-in_binary64_1399` `associate--l+_binary64_1379` `associate-+r-_binary64_1376` `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` `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` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `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_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-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_1385` `associate-*r/_binary64_1384` `associate--l-_binary64_1380`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

prune2.0ms (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

16.6b

Counts

1 → 1

Compiler

Compiled 19 to 17 computations (10.5% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
2.1b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite120.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

3.9b

Rules

11×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
10×	`add-sqr-sqrt_binary64_1464`
8×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`associate-r_binary64_1382`
4×	`cos-sum_binary64_1576` `add-log-exp_binary64_1481` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `associate-l_binary64_1383`
3×	`cos-diff_binary64_1579` `cancel-sign-sub-inv_binary64_1408`
2×	`*-commutative_binary64_1373`
1×	`sub-neg_binary64_1435` `acos-asin_binary64_1623` `unswap-sqr_binary64_1410` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `cos-mult_binary64_1596` `associate-*l/_binary64_1385`

Counts

4 → 59

Calls

4 calls:

8.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
6.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 1775 to 321 computations (81.9% saved)

series1.2s (5.2%)

Error

15.9b

Counts

4 → 59

Calls

4 calls:

585.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
366.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
151.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
78.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 3613 to 2076 computations (42.5% saved)

simplify185.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

504×	`distribute-rgt-neg-in_binary64_1400`
438×	`distribute-lft-neg-in_binary64_1399`
360×	`cancel-sign-sub-inv_binary64_1408`
292×	`neg-mul-1_binary64_1438`
276×	`neg-sub0_binary64_1437`
263×	`associate-l_binary64_1383`
260×	`associate-r_binary64_1382`
239×	`sub-neg_binary64_1435`
163×	`unsub-neg_binary64_1436`
153×	`*-commutative_binary64_1373`
139×	`distribute-rgt-out--_binary64_1396`
126×	`distribute-lft-in_binary64_1391`
110×	`distribute-rgt-out_binary64_1395`
95×	`distribute-rgt-in_binary64_1392`
94×	`distribute-lft-out--_binary64_1394`
85×	`sqr-pow_binary64_1414`
65×	`+-commutative_binary64_1372`
61×	`distribute-lft-neg-out_binary64_1401`
58×	`distribute-lft-out_binary64_1393`
43×	`unswap-sqr_binary64_1410`
39×	`distribute-rgt-neg-out_binary64_1402`
37×	`exp-prod_binary64_1494`
36×	`associate--l+_binary64_1379` `associate-+l-_binary64_1377`
35×	`associate-+l+_binary64_1375`
33×	`log-prod_binary64_1528`
32×	`cube-prod_binary64_1470`
31×	`associate-+r-_binary64_1376`
30×	`swap-sqr_binary64_1409`
29×	`cancel-sign-sub_binary64_1407`
25×	`associate-+r+_binary64_1374`
24×	`*-rgt-identity_binary64_1432`
23×	`associate--l-_binary64_1380` `associate--r+_binary64_1378`
21×	`remove-double-neg_binary64_1430`
20×	`*-lft-identity_binary64_1431` `+-rgt-identity_binary64_1427`
19×	`sub0-neg_binary64_1429`
15×	`pow-sqr_binary64_1415`
14×	`cube-unmult_binary64_1479` `associate--r-_binary64_1381`
13×	`distribute-neg-in_binary64_1403`
12×	`unpow3_binary64_1508` `rem-sqrt-square_binary64_1455`
10×	`associate-/l*_binary64_1387`
9×	`unpow1/2_binary64_1506` `distribute-rgt1-in_binary64_1398`
7×	`cube-mult_binary64_1472`
6×	`cos-neg_binary64_1573` `difference-of-squares_binary64_1411`
5×	`sin-neg_binary64_1572`
4×	`unpow2_binary64_1507` `unpow1_binary64_1500` `distribute-lft1-in_binary64_1397`
3×	`pow-plus_binary64_1505`
2×	`exp-sum_binary64_1488` `mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `distribute-neg-out_binary64_1404` `associate-/l/_binary64_1389` `associate-*r/_binary64_1384`
1×	`1-exp_binary64_1486` `exp-1-e_binary64_1485` `rem-3cbrt-lft_binary64_1467` `sqr-neg_binary64_1456` `rem-square-sqrt_binary64_1454` `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` `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` `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` `prod-exp_binary64_1491` `exp-diff_binary64_1490` `exp-neg_binary64_1489` `e-exp-1_binary64_1487` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `cube-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` `times-frac_binary64_1448` `div-sub_binary64_1447` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `--rgt-identity_binary64_1428` `+-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-sqr--1_binary64_1413` `difference-of-sqr-1_binary64_1412` `distribute-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `associate-/r/_binary64_1388` `associate-/r_binary64_1386` `associate-*l/_binary64_1385`

Counts

118 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3344
1	482	2978
2	1510	2896
3	2689	2862
4	4761	2862
5	4996	2862
6	4957	2862

prune117.0ms (0.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	45	13	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	13	59

Error

3.9b

Counts

59 → 13

Compiler

Compiled 2022 to 591 computations (70.8% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
2.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite122.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

3.8b

Rules

16×	`add-sqr-sqrt_binary64_1464`
10×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`associate-l_binary64_1383` `associate-r_binary64_1382`
4×	`add-log-exp_binary64_1481`
3×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`
2×	`sin-mult_binary64_1597`
1×	`acos-asin_binary64_1623`

Counts

4 → 64

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2362 to 361 computations (84.7% saved)

series1.1s (4.4%)

Error

3.9b

Counts

4 → 44

Calls

4 calls:

527.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
202.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
138.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
137.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 3948 to 2061 computations (47.8% saved)

simplify214.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

370×	`sub-neg_binary64_1435`
354×	`cancel-sign-sub-inv_binary64_1408` `distribute-rgt-neg-in_binary64_1400`
332×	`*-commutative_binary64_1373`
242×	`sqr-pow_binary64_1414`
240×	`neg-mul-1_binary64_1438`
238×	`distribute-lft-neg-in_binary64_1399`
236×	`unsub-neg_binary64_1436`
222×	`neg-sub0_binary64_1437`
170×	`associate-+l+_binary64_1375`
169×	`associate-l_binary64_1383`
161×	`distribute-neg-in_binary64_1403`
154×	`associate-r_binary64_1382`
119×	`associate--l+_binary64_1379`
117×	`distribute-lft-out--_binary64_1394`
110×	`associate-+r+_binary64_1374`
104×	`distribute-lft-neg-out_binary64_1401`
98×	`+-commutative_binary64_1372`
97×	`associate-+l-_binary64_1377`
90×	`log-prod_binary64_1528` `pow-sqr_binary64_1415`
87×	`associate-/l/_binary64_1389`
86×	`distribute-lft-out_binary64_1393` `distribute-rgt-in_binary64_1392`
85×	`log-div_binary64_1529` `cube-div_binary64_1471`
81×	`distribute-rgt-out--_binary64_1396`
80×	`associate--r+_binary64_1378`
79×	`cube-prod_binary64_1470`
75×	`exp-prod_binary64_1494`
70×	`remove-double-neg_binary64_1430`
69×	`associate-/l*_binary64_1387` `associate--r-_binary64_1381`
65×	`distribute-rgt-neg-out_binary64_1402`
56×	`cancel-sign-sub_binary64_1407` `distribute-rgt-out_binary64_1395`
55×	`distribute-lft-in_binary64_1391`
51×	`-rgt-identity_binary64_1432` `associate-r/_binary64_1384`
43×	`associate-+r-_binary64_1376`
42×	`associate-/r/_binary64_1388`
41×	`sub0-neg_binary64_1429`
37×	`associate--l-_binary64_1380`
36×	`unswap-sqr_binary64_1410`
33×	`rem-sqrt-square_binary64_1455`
32×	`unpow3_binary64_1508`
31×	`cube-mult_binary64_1472`
30×	`*-lft-identity_binary64_1431`
28×	`times-frac_binary64_1448` `+-rgt-identity_binary64_1427`
27×	`mul0-rgt_binary64_1425` `mul0-lft_binary64_1424`
24×	`swap-sqr_binary64_1409`
23×	`associate-/r*_binary64_1386`
15×	`div-sub_binary64_1447`
12×	`exp-sqrt_binary64_1495`
10×	`cube-unmult_binary64_1479`
9×	`unpow1/2_binary64_1506` `--rgt-identity_binary64_1428`
8×	`distribute-neg-out_binary64_1404`
6×	`cos-neg_binary64_1573` `sin-neg_binary64_1572` `log-rec_binary64_1530` `exp-lft-sqr_binary64_1497`
5×	`sqr-neg_binary64_1456` `distribute-rgt1-in_binary64_1398`
4×	`exp-diff_binary64_1490` `exp-sum_binary64_1488` `cube-neg_binary64_1469` `distribute-lft1-in_binary64_1397`
3×	`prod-exp_binary64_1491` `/-rgt-identity_binary64_1433` `distribute-frac-neg_binary64_1405` `associate-*l/_binary64_1385`
2×	`exp-neg_binary64_1489`
1×	`1-exp_binary64_1486` `exp-1-e_binary64_1485` `mul-1-neg_binary64_1434` `div0_binary64_1423` `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` `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` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `unpow2_binary64_1507` `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-cbrt_binary64_1496` `div-exp_binary64_1493` `rec-exp_binary64_1492` `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` `rem-square-sqrt_binary64_1454` `+-lft-identity_binary64_1426` `*-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` `difference-of-squares_binary64_1411` `distribute-neg-frac_binary64_1406`

Counts

108 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	3351
1	343	2998
2	946	2983
3	1386	2983
4	2213	2983
5	3327	2983
6	4205	2983
7	4629	2983
8	4863	2983

prune143.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	64	10	74
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	73	14	87

Error

3.8b

Counts

87 → 14

Compiler

Compiled 2908 to 622 computations (78.6% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
2.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
4.7b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))

rewrite111.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

3.8b

Rules

13×	`add-sqr-sqrt_binary64_1464`
9×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`associate-l_binary64_1383` `associate-r_binary64_1382`
5×	`add-log-exp_binary64_1481`
3×	`log-pow_binary64_1531` `log-prod_binary64_1528`
2×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`
1×	`exp-to-pow_binary64_1504` `exp-prod_binary64_1494` `rem-log-exp_binary64_1483` `acos-asin_binary64_1623` `sin-mult_binary64_1597`

Counts

4 → 59

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))

Compiler

Compiled 2357 to 375 computations (84.1% saved)

series1.4s (6%)

Error

3.8b

Counts

4 → 45

Calls

4 calls:

583.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
394.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
235.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
145.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 4232 to 2247 computations (46.9% saved)

simplify183.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

389×	`cancel-sign-sub-inv_binary64_1408`
326×	`neg-mul-1_binary64_1438`
307×	`neg-sub0_binary64_1437` `associate-l_binary64_1383`
275×	`distribute-rgt-neg-in_binary64_1400`
261×	`distribute-rgt-in_binary64_1392` `*-commutative_binary64_1373`
259×	`sub-neg_binary64_1435`
247×	`distribute-lft-in_binary64_1391`
233×	`distribute-lft-neg-in_binary64_1399`
230×	`associate-r_binary64_1382`
146×	`associate-+l+_binary64_1375`
138×	`sqr-pow_binary64_1414`
115×	`log-prod_binary64_1528` `distribute-lft-neg-out_binary64_1401`
114×	`distribute-neg-in_binary64_1403`
111×	`associate-+r+_binary64_1374`
102×	`distribute-rgt-neg-out_binary64_1402`
87×	`unsub-neg_binary64_1436`
84×	`cancel-sign-sub_binary64_1407`
81×	`associate-+l-_binary64_1377`
73×	`+-commutative_binary64_1372`
72×	`unswap-sqr_binary64_1410`
61×	`associate--r+_binary64_1378`
55×	`exp-prod_binary64_1494`
54×	`log-pow_binary64_1531` `distribute-lft-out_binary64_1393` `associate--l+_binary64_1379`
51×	`cube-prod_binary64_1470`
48×	`*-lft-identity_binary64_1431`
47×	`distribute-lft-out--_binary64_1394`
46×	`exp-sum_binary64_1488`
44×	`*-rgt-identity_binary64_1432` `pow-sqr_binary64_1415`
41×	`distribute-rgt-out_binary64_1395`
35×	`associate-+r-_binary64_1376`
33×	`sub0-neg_binary64_1429`
31×	`mul0-rgt_binary64_1425` `mul0-lft_binary64_1424`
29×	`count-2_binary64_1390`
28×	`distribute-rgt-out--_binary64_1396`
27×	`log-div_binary64_1529`
25×	`cube-div_binary64_1471` `remove-double-neg_binary64_1430`
24×	`unpow3_binary64_1508`
23×	`swap-sqr_binary64_1409`
22×	`rem-sqrt-square_binary64_1455`
20×	`cube-unmult_binary64_1479` `+-rgt-identity_binary64_1427` `associate-/l*_binary64_1387`
19×	`associate--l-_binary64_1380`
18×	`exp-to-pow_binary64_1504`
16×	`cube-mult_binary64_1472`
15×	`distribute-neg-out_binary64_1404` `associate--r-_binary64_1381`
14×	`div-sub_binary64_1447` `associate-/l/_binary64_1389`
12×	`cube-neg_binary64_1469`
11×	`sqr-neg_binary64_1456`
10×	`pow-plus_binary64_1505`
9×	`rem-exp-log_binary64_1482`
8×	`exp-sqrt_binary64_1495` `exp-neg_binary64_1489` `associate-*r/_binary64_1384`
6×	`unpow1/2_binary64_1506`
5×	`exp-diff_binary64_1490` `rem-log-exp_binary64_1483` `--rgt-identity_binary64_1428`
4×	`log-rec_binary64_1530` `distribute-frac-neg_binary64_1405` `associate-/r/_binary64_1388` `associate-/r_binary64_1386` `associate-l/_binary64_1385`
3×	`unpow2_binary64_1507` `exp-lft-sqr_binary64_1497` `distribute-rgt1-in_binary64_1398`
2×	`cos-neg_binary64_1573` `/-rgt-identity_binary64_1433` `+-lft-identity_binary64_1426` `distribute-lft1-in_binary64_1397`
1×	`sin-neg_binary64_1572` `log-E_binary64_1532` `1-exp_binary64_1486` `exp-1-e_binary64_1485`
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` `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` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `pow-base-1_binary64_1502` `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-3cbrt-rft_binary64_1468` `rem-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `rem-square-sqrt_binary64_1454` `times-frac_binary64_1448` `mul-1-neg_binary64_1434` `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` `difference-of-squares_binary64_1411` `distribute-neg-frac_binary64_1406`

Counts

104 → 87

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	133	3352
1	251	2995
2	627	2975
3	1169	2975
4	1911	2975
5	3785	2969
6	4380	2969
7	4875	2969

prune146.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	87	14	101

Error

3.8b

Counts

101 → 14

Compiler

Compiled 3351 to 713 computations (78.7% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))
2.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1))))))))

rewrite83.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

3.8b

Rules

9×	`cbrt-prod_binary64_1473`
7×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
4×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
3×	`pow1/3_binary64_1524`
1×	`acos-asin_binary64_1623`

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt.f64 (sin.f64 lambda1))
2.0ms	(cbrt.f64 (sin.f64 lambda1))
2.0ms	(cbrt.f64 (sin.f64 lambda1))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1))))))))

Compiler

Compiled 1785 to 327 computations (81.7% saved)

series552.0ms (2.3%)

Error

3.8b

Counts

4 → 21

Calls

4 calls:

243.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1))))))))
102.0ms	(cbrt.f64 (sin.f64 lambda1))
93.0ms	(cbrt.f64 (sin.f64 lambda1))
87.0ms	(cbrt.f64 (sin.f64 lambda1))

Compiler

Compiled 2139 to 1167 computations (45.4% saved)

simplify139.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

574×	`log-prod_binary64_1528`
513×	`associate-/l/_binary64_1389`
412×	`associate-/r/_binary64_1388`
403×	`*-commutative_binary64_1373`
328×	`unswap-sqr_binary64_1410`
292×	`associate-/l*_binary64_1387`
210×	`+-commutative_binary64_1372`
187×	`sqr-pow_binary64_1414`
183×	`associate-l_binary64_1383`
166×	`distribute-rgt-in_binary64_1392`
162×	`distribute-lft-in_binary64_1391`
157×	`associate-r_binary64_1382`
152×	`associate-+l+_binary64_1375`
143×	`count-2_binary64_1390`
136×	`distribute-rgt-out_binary64_1395`
135×	`associate-+r+_binary64_1374`
100×	`log-pow_binary64_1531` `times-frac_binary64_1448`
97×	`distribute-lft-out_binary64_1393`
78×	`pow-sqr_binary64_1415`
76×	`log-div_binary64_1529`
66×	`distribute-rgt1-in_binary64_1398`
43×	`exp-prod_binary64_1494`
41×	`rem-sqrt-square_binary64_1455`
33×	`associate-*r/_binary64_1384`
30×	`cube-prod_binary64_1470`
29×	`distribute-lft1-in_binary64_1397`
21×	`pow-plus_binary64_1505`
20×	`associate-/r*_binary64_1386`
18×	`associate-*l/_binary64_1385`
15×	`unpow3_binary64_1508`
13×	`cube-unmult_binary64_1479`
10×	`cube-mult_binary64_1472`
6×	`unpow2_binary64_1507`
4×	`unpow1_binary64_1500` `/-rgt-identity_binary64_1433` `*-lft-identity_binary64_1431`
2×	`unpow1/3_binary64_1509` `swap-sqr_binary64_1409`
1×	`log-rec_binary64_1530` `unpow1/2_binary64_1506` `1-exp_binary64_1486` `rem-3cbrt-lft_binary64_1467`
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` `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` `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-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` `neg-mul-1_binary64_1438` `neg-sub0_binary64_1437` `unsub-neg_binary64_1436` `sub-neg_binary64_1435` `mul-1-neg_binary64_1434` `-rgt-identity_binary64_1432` `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` `difference-of-squares_binary64_1411` `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-rgt-out--_binary64_1396` `distribute-lft-out--_binary64_1394` `associate--r-_binary64_1381` `associate--l-_binary64_1380` `associate--l+_binary64_1379` `associate--r+_binary64_1378` `associate-+l-_binary64_1377` `associate-+r-_binary64_1376`

Counts

62 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	1571
1	101	1176
2	224	1176
3	562	1176
4	742	1176
5	1602	1176
6	2188	1176
7	2945	1176
8	4681	1176
9	4953	1176

prune45.0ms (0.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	32	15	47

Error

3.8b

Counts

47 → 15

Compiler

Compiled 1102 to 111 computations (89.9% saved)

regimes3.8s (15.8%)

Accuracy

Total 0.4b remaining (9.9%)

Threshold costs 0.4b (9.9%)

Compiler

Compiled 48482 to 29842 computations (38.4% saved)

bsearch0.0ms (0%)

simplify28.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64_1373`
2×	`+-commutative_binary64_1372`
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` `neg-mul-1_binary64_1438` `neg-sub0_binary64_1437` `unsub-neg_binary64_1436` `sub-neg_binary64_1435` `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	23	43
1	31	43
2	31	43

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 104 to 88 computations (15.4% saved)

end0.0ms (0%)

sample10.1s (42.7%)

Algorithm

1×

intervals

Results

4.8s	5523×	body	1024	valid
731.0ms	1383×	body	512	valid
528.0ms	285×	body	2048	valid
174.0ms	505×	body	256	valid
55.0ms	304×	body	128	valid
2.0ms	2×	body	1024	invalid

Compiler

Compiled 4402 to 2744 computations (37.7% saved)

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

Details

analyze3.6s (15.2%)

sample224.0ms (0.9%)

simplify13.0ms (0.1%)

prune2.0ms (0%)

localize25.0ms (0.1%)

rewrite120.0ms (0.5%)

series1.2s (5.2%)

simplify185.0ms (0.8%)

prune117.0ms (0.5%)

localize29.0ms (0.1%)

rewrite122.0ms (0.5%)

series1.1s (4.4%)

simplify214.0ms (0.9%)

prune143.0ms (0.6%)

localize29.0ms (0.1%)

rewrite111.0ms (0.5%)

series1.4s (6%)

simplify183.0ms (0.8%)

prune146.0ms (0.6%)

localize30.0ms (0.1%)

rewrite83.0ms (0.3%)

series552.0ms (2.3%)

simplify139.0ms (0.6%)

prune45.0ms (0.2%)

regimes3.8s (15.8%)

bsearch0.0ms (0%)

simplify28.0ms (0.1%)

end0.0ms (0%)

sample10.1s (42.7%)

Profiling

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31