Details

analyze2.9s (11.9%)

Algorithm

1×

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

Compiler

Compiled 20 to 18 computations (10% saved)

sample221.0ms (0.9%)

Algorithm

1×

intervals

Results

166.0ms	193×	body	1024	valid
19.0ms	37×	body	512	valid
7.0ms	2×	body	2048	valid
4.0ms	13×	body	256	valid
2.0ms	11×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify109.0ms (0.5%)

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

prune3.0ms (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

15.3b

Counts

1 → 1

Compiler

Compiled 19 to 17 computations (10.5% saved)

localize19.0ms (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)
1.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.7b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite101.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

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:

7.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(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)

series844.0ms (3.5%)

Error

14.5b

Counts

4 → 61

Calls

4 calls:

388.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
238.0ms	(.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)
105.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
56.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 3773 to 2153 computations (42.9% saved)

simplify151.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

551×	`distribute-rgt-neg-in_binary64_1400`
483×	`distribute-lft-neg-in_binary64_1399`
447×	`cancel-sign-sub-inv_binary64_1408`
327×	`neg-mul-1_binary64_1438`
286×	`sub-neg_binary64_1435`
279×	`associate-r_binary64_1382`
278×	`associate-l_binary64_1383`
221×	`neg-sub0_binary64_1437`
191×	`distribute-lft-out--_binary64_1394`
163×	`*-commutative_binary64_1373`
155×	`distribute-rgt-out--_binary64_1396`
125×	`distribute-rgt-out_binary64_1395`
91×	`sqr-pow_binary64_1414`
78×	`+-commutative_binary64_1372`
63×	`distribute-lft-neg-out_binary64_1401`
57×	`unsub-neg_binary64_1436`
55×	`unswap-sqr_binary64_1410`
46×	`associate--l+_binary64_1379`
44×	`associate-+l-_binary64_1377`
40×	`associate-+l+_binary64_1375`
39×	`distribute-rgt-neg-out_binary64_1402`
38×	`associate-+r-_binary64_1376`
37×	`exp-prod_binary64_1494`
35×	`cube-prod_binary64_1470`
33×	`log-prod_binary64_1528`
32×	`swap-sqr_binary64_1409`
31×	`cancel-sign-sub_binary64_1407` `associate-+r+_binary64_1374`
29×	`associate--r+_binary64_1378`
24×	`*-rgt-identity_binary64_1432` `+-rgt-identity_binary64_1427`
22×	`sub0-neg_binary64_1429`
21×	`remove-double-neg_binary64_1430`
20×	`*-lft-identity_binary64_1431`
17×	`cube-unmult_binary64_1479`
16×	`pow-sqr_binary64_1415` `distribute-rgt-in_binary64_1392`
15×	`distribute-neg-in_binary64_1403`
12×	`unpow3_binary64_1508` `rem-sqrt-square_binary64_1455`
9×	`unpow1/2_binary64_1506` `distribute-rgt1-in_binary64_1398`
6×	`cos-neg_binary64_1573` `difference-of-squares_binary64_1411` `distribute-lft-out_binary64_1393`
5×	`pow-plus_binary64_1505` `cube-mult_binary64_1472`
4×	`sin-neg_binary64_1572` `unpow2_binary64_1507` `unpow1_binary64_1500` `distribute-lft1-in_binary64_1397` `distribute-lft-in_binary64_1391`
2×	`exp-sum_binary64_1488` `mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `distribute-neg-out_binary64_1404`
1×	`1-exp_binary64_1486` `exp-1-e_binary64_1485` `rem-3cbrt-lft_binary64_1467` `sqr-neg_binary64_1456` `rem-square-sqrt_binary64_1454` `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` `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` `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--r-_binary64_1381`

Counts

120 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	3476
1	521	3110
2	1636	2994
3	2984	2962
4	4883	2962
5	4973	2962

prune198.0ms (0.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Error

1.9b

Counts

132 → 13

Compiler

Compiled 4915 to 1174 computations (76.1% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.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)
0.9b	(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))))))

rewrite144.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

13×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `add-sqr-sqrt_binary64_1464`
9×	`add-cube-cbrt_binary64_1477` `-un-lft-identity_binary64_1442` `associate-r*_binary64_1382`
7×	`associate-l_binary64_1383`
6×	`cos-mult_binary64_1596`
5×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
4×	`add-log-exp_binary64_1481`
3×	`-commutative_binary64_1373` `sin-mult_binary64_1597` `frac-times_binary64_1452` `associate-r/_binary64_1384`
2×	`unswap-sqr_binary64_1410` `frac-add_binary64_1450` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`acos-asin_binary64_1623` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `associate-*l/_binary64_1385`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
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 2888 to 452 computations (84.3% saved)

series1.4s (5.8%)

Error

1.9b

Counts

4 → 59

Calls

4 calls:

706.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
365.0ms	(.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)
164.0ms	(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))))))
89.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 5570 to 2822 computations (49.3% saved)

simplify173.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

526×	`associate-r_binary64_1382`
496×	`associate-l_binary64_1383`
338×	`distribute-rgt-neg-in_binary64_1400`
307×	`distribute-lft-neg-in_binary64_1399`
287×	`neg-mul-1_binary64_1438`
247×	`*-commutative_binary64_1373`
201×	`distribute-rgt-out_binary64_1395`
152×	`exp-prod_binary64_1494`
151×	`sub-neg_binary64_1435`
94×	`distribute-rgt-in_binary64_1392`
91×	`distribute-lft-in_binary64_1391`
90×	`+-commutative_binary64_1372`
89×	`cancel-sign-sub-inv_binary64_1408`
70×	`sqr-pow_binary64_1414`
63×	`neg-sub0_binary64_1437`
60×	`associate--l+_binary64_1379`
57×	`distribute-rgt-out--_binary64_1396`
50×	`distribute-neg-in_binary64_1403`
44×	`cube-prod_binary64_1470`
42×	`log-prod_binary64_1528` `associate--r+_binary64_1378` `associate-+l+_binary64_1375`
39×	`*-rgt-identity_binary64_1432`
38×	`*-lft-identity_binary64_1431`
34×	`associate-+r+_binary64_1374`
30×	`distribute-lft-neg-out_binary64_1401`
27×	`unsub-neg_binary64_1436` `swap-sqr_binary64_1409`
23×	`distribute-lft-out--_binary64_1394`
19×	`unswap-sqr_binary64_1410`
14×	`unpow3_binary64_1508`
13×	`cube-unmult_binary64_1479`
10×	`distribute-lft-out_binary64_1393`
9×	`cube-mult_binary64_1472`
8×	`exp-sum_binary64_1488`
7×	`unpow1/2_binary64_1506` `distribute-rgt-neg-out_binary64_1402`
4×	`unpow2_binary64_1507` `unpow1_binary64_1500` `rem-sqrt-square_binary64_1455` `difference-of-squares_binary64_1411`
3×	`pow-plus_binary64_1505` `pow-sqr_binary64_1415` `distribute-rgt1-in_binary64_1398`
1×	`1-exp_binary64_1486` `exp-1-e_binary64_1485` `distribute-lft1-in_binary64_1397` `associate-+l-_binary64_1377` `associate-+r-_binary64_1376`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1705` `erf-erfc_binary64_1704` `erf-odd_binary64_1703` `if-if-and-not_binary64_1702` `if-if-and_binary64_1701` `if-if-or-not_binary64_1700` `if-if-or_binary64_1699` `if-not_binary64_1698` `if-same_binary64_1697` `if-false_binary64_1696` `if-true_binary64_1695` `not-gte_binary64_1694` `not-lte_binary64_1693` `not-gt_binary64_1692` `not-lt_binary64_1691` `gte-same_binary64_1690` `lte-same_binary64_1689` `gt-same_binary64_1688` `lt-same_binary64_1687` `sinh---cosh_binary64_1634` `sinh-+-cosh_binary64_1633` `sinh-cosh_binary64_1632` `tanh-def-c_binary64_1631` `tanh-def-b_binary64_1630` `tanh-def-a_binary64_1629` `cosh-def_binary64_1628` `sinh-def_binary64_1627` `tan-neg_binary64_1574` `cos-neg_binary64_1573` `sin-neg_binary64_1572` `tan-0_binary64_1571` `cos-0_binary64_1570` `sin-0_binary64_1569` `hang-m-tan_binary64_1568` `hang-p-tan_binary64_1567` `hang-m0-tan_binary64_1566` `hang-p0-tan_binary64_1565` `hang-0m-tan_binary64_1564` `hang-0p-tan_binary64_1563` `tan-+PI/2_binary64_1562` `tan-+PI_binary64_1561` `tan-PI_binary64_1560` `tan-PI/3_binary64_1559` `tan-PI/4_binary64_1558` `tan-PI/6_binary64_1557` `cos-+PI/2_binary64_1556` `cos-+PI_binary64_1555` `cos-PI_binary64_1554` `cos-PI/2_binary64_1553` `cos-PI/3_binary64_1552` `cos-PI/4_binary64_1551` `cos-PI/6_binary64_1550` `sin-+PI/2_binary64_1549` `sin-+PI_binary64_1548` `sin-PI_binary64_1547` `sin-PI/2_binary64_1546` `sin-PI/3_binary64_1545` `sin-PI/4_binary64_1544` `sin-PI/6_binary64_1543` `sub-1-sin_binary64_1542` `sub-1-cos_binary64_1541` `-1-add-sin_binary64_1540` `-1-add-cos_binary64_1539` `1-sub-sin_binary64_1538` `1-sub-cos_binary64_1537` `cos-sin-sum_binary64_1536` `log-E_binary64_1532` `log-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-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `rem-square-sqrt_binary64_1454` `times-frac_binary64_1448` `div-sub_binary64_1447` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `remove-double-neg_binary64_1430` `sub0-neg_binary64_1429` `--rgt-identity_binary64_1428` `+-rgt-identity_binary64_1427` `+-lft-identity_binary64_1426` `mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `div0_binary64_1423` `-inverses_binary64_1422` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `remove-double-div_binary64_1418` `difference-of-sqr--1_binary64_1413` `difference-of-sqr-1_binary64_1412` `cancel-sign-sub_binary64_1407` `distribute-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `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--r-_binary64_1381` `associate--l-_binary64_1380`

Counts

131 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	290	5385
1	822	4730
2	3177	4649
3	4832	4649
4	5133	4649

prune255.0ms (1.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	150	14	164
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	162	15	177

Error

1.8b

Counts

177 → 15

Compiler

Compiled 7808 to 1549 computations (80.2% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) R)
0.3b	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
0.9b	(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)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))))))
28.9b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))

rewrite127.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

10×	`add-sqr-sqrt_binary64_1464`
9×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
8×	`add-cube-cbrt_binary64_1477` `cbrt-prod_binary64_1473` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481`
3×	`pow-unpow_binary64_1519` `associate-l_binary64_1383` `associate-r_binary64_1382`
2×	`sin-mult_binary64_1597` `cube-div_binary64_1471` `unpow-prod-down_binary64_1521` `unpow3_binary64_1508` `cube-mult_binary64_1472` `cube-prod_binary64_1470` `sqr-pow_binary64_1414` `pow-prod-down_binary64_1513` `pow-pow_binary64_1514` `prod-exp_binary64_1491` `pow-exp_binary64_1510` `rem-cube-cbrt_binary64_1465` `cbrt-unprod_binary64_1475`
1×	`pow1/3_binary64_1524` `cbrt-div_binary64_1474` `rem-cbrt-cube_binary64_1466` `acos-asin_binary64_1623` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`

Counts

4 → 67

Calls

4 calls:

5.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
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)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) R)
3.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))
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)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))))))

Compiler

Compiled 2752 to 882 computations (68% saved)

series861.0ms (3.6%)

Error

1.8b

Counts

4 → 45

Calls

4 calls:

366.0ms	(.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)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) R)
180.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
156.0ms	(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)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))))))
107.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))

Compiler

Compiled 4141 to 2254 computations (45.6% saved)

simplify179.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

496×	`unswap-sqr_binary64_1410`
412×	`cancel-sign-sub-inv_binary64_1408`
375×	`*-commutative_binary64_1373`
269×	`log-prod_binary64_1528`
216×	`exp-prod_binary64_1494`
199×	`distribute-rgt-neg-in_binary64_1400`
193×	`distribute-lft-neg-in_binary64_1399`
167×	`sqr-pow_binary64_1414`
136×	`associate-r_binary64_1382`
129×	`associate-l_binary64_1383`
121×	`sub-neg_binary64_1435`
109×	`cube-prod_binary64_1470`
101×	`swap-sqr_binary64_1409`
84×	`distribute-rgt-in_binary64_1392`
80×	`distribute-lft-in_binary64_1391`
73×	`distribute-rgt-out_binary64_1395`
72×	`distribute-lft-out--_binary64_1394` `distribute-lft-out_binary64_1393`
66×	`neg-mul-1_binary64_1438` `neg-sub0_binary64_1437`
65×	`distribute-rgt-out--_binary64_1396`
53×	`unpow3_binary64_1508`
38×	`+-commutative_binary64_1372`
36×	`log-pow_binary64_1531`
35×	`pow-sqr_binary64_1415`
26×	`cube-mult_binary64_1472`
24×	`associate--l+_binary64_1379` `associate-+l+_binary64_1375`
21×	`pow-plus_binary64_1505`
20×	`unsub-neg_binary64_1436` `associate-+l-_binary64_1377` `associate-+r+_binary64_1374`
16×	`distribute-lft-neg-out_binary64_1401` `associate-+r-_binary64_1376`
12×	`distribute-rgt-neg-out_binary64_1402` `associate--r+_binary64_1378`
11×	`cube-unmult_binary64_1479`
10×	`sub0-neg_binary64_1429` `+-rgt-identity_binary64_1427`
9×	`*-lft-identity_binary64_1431`
8×	`*-rgt-identity_binary64_1432` `distribute-neg-in_binary64_1403`
5×	`rem-cbrt-cube_binary64_1466` `rem-sqrt-square_binary64_1455`
3×	`unpow1/2_binary64_1506` `associate-/l/_binary64_1389` `associate-*r/_binary64_1384`
2×	`count-2_binary64_1390`
1×	`cos-neg_binary64_1573` `unpow1_binary64_1500` `1-exp_binary64_1486` `exp-1-e_binary64_1485` `rem-3cbrt-lft_binary64_1467` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `distribute-rgt1-in_binary64_1398` `distribute-lft1-in_binary64_1397` `associate-/r/_binary64_1388` `associate-/l*_binary64_1387`
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-rec_binary64_1530` `log-div_binary64_1529` `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` `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-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-cube-cbrt_binary64_1465` `rem-square-sqrt_binary64_1454` `times-frac_binary64_1448` `div-sub_binary64_1447` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `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_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_binary64_1407` `distribute-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `associate-/r_binary64_1386` `associate-*l/_binary64_1385` `associate--r-_binary64_1381` `associate--l-_binary64_1380`

Counts

112 → 170

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	157	3532
1	332	3173
2	1044	3147
3	2150	3135
4	4705	3132
5	4987	3132
6	4966	3132

prune247.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	170	15	185

Error

1.8b

Counts

185 → 15

Compiler

Compiled 7221 to 1915 computations (73.5% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

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 lambda2) (cbrt.f64 (pow.f64 (sin.f64 lambda1) 3))))))) R)
0.4b	(pow.f64 (sin.f64 lambda1) 3)
0.9b	(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 lambda2) (cbrt.f64 (pow.f64 (sin.f64 lambda1) 3)))))))
19.2b	(cbrt.f64 (pow.f64 (sin.f64 lambda1) 3))

rewrite127.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

14×	`add-sqr-sqrt_binary64_1464`
12×	`add-cube-cbrt_binary64_1477` `cbrt-prod_binary64_1473` `*-un-lft-identity_binary64_1442`
7×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`unpow-prod-down_binary64_1521` `cube-prod_binary64_1470`
4×	`add-log-exp_binary64_1481`
3×	`pow-unpow_binary64_1519` `associate-l_binary64_1383` `associate-r_binary64_1382`
2×	`unpow3_binary64_1508` `cube-mult_binary64_1472` `sqr-pow_binary64_1414`
1×	`pow1/3_binary64_1524` `rem-cbrt-cube_binary64_1466` `acos-asin_binary64_1623` `pow-pow_binary64_1514` `pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `rem-cube-cbrt_binary64_1465` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`

Counts

4 → 70

Calls

4 calls:

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 lambda2) (cbrt.f64 (pow.f64 (sin.f64 lambda1) 3))))))) R)
4.0ms	(pow.f64 (sin.f64 lambda1) 3)
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 lambda1) 3))
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 lambda2) (cbrt.f64 (pow.f64 (sin.f64 lambda1) 3)))))))

Compiler

Compiled 2816 to 1001 computations (64.5% saved)

series596.0ms (2.5%)

Error

1.8b

Counts

4 → 33

Calls

4 calls:

368.0ms	(.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 lambda2) (cbrt.f64 (pow.f64 (sin.f64 lambda1) 3))))))) R)
150.0ms	(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 lambda2) (cbrt.f64 (pow.f64 (sin.f64 lambda1) 3)))))))
31.0ms	(pow.f64 (sin.f64 lambda1) 3)
15.0ms	(cbrt.f64 (pow.f64 (sin.f64 lambda1) 3))

Compiler

Compiled 3093 to 1593 computations (48.5% saved)

simplify141.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-l_binary64_1383`
573×	`sqr-pow_binary64_1414`
471×	`associate-r_binary64_1382`
412×	`log-prod_binary64_1528`
387×	`exp-prod_binary64_1494`
348×	`cube-prod_binary64_1470`
231×	`unswap-sqr_binary64_1410`
157×	`pow-sqr_binary64_1415`
151×	`swap-sqr_binary64_1409`
127×	`unpow3_binary64_1508`
112×	`*-commutative_binary64_1373`
104×	`cube-mult_binary64_1472`
63×	`associate-/l*_binary64_1387`
56×	`distribute-rgt-in_binary64_1392`
55×	`pow-plus_binary64_1505`
52×	`distribute-lft-in_binary64_1391` `associate-+l+_binary64_1375`
49×	`log-pow_binary64_1531`
47×	`associate-+r+_binary64_1374`
24×	`cube-unmult_binary64_1479` `-rgt-identity_binary64_1432` `-lft-identity_binary64_1431`
20×	`distribute-rgt-out_binary64_1395`
12×	`count-2_binary64_1390` `associate-/l/_binary64_1389`
11×	`rem-sqrt-square_binary64_1455`
10×	`+-commutative_binary64_1372`
7×	`distribute-lft-out_binary64_1393` `associate-*r/_binary64_1384`
4×	`rem-cbrt-cube_binary64_1466`
3×	`unpow2_binary64_1507` `unpow1/2_binary64_1506` `associate-*l/_binary64_1385`
2×	`/-rgt-identity_binary64_1433` `associate-/r/_binary64_1388`
1×	`unpow1_binary64_1500` `1-exp_binary64_1486` `exp-1-e_binary64_1485` `rem-3cbrt-lft_binary64_1467` `rem-cube-cbrt_binary64_1465` `rem-square-sqrt_binary64_1454` `times-frac_binary64_1448`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1705` `erf-erfc_binary64_1704` `erf-odd_binary64_1703` `if-if-and-not_binary64_1702` `if-if-and_binary64_1701` `if-if-or-not_binary64_1700` `if-if-or_binary64_1699` `if-not_binary64_1698` `if-same_binary64_1697` `if-false_binary64_1696` `if-true_binary64_1695` `not-gte_binary64_1694` `not-lte_binary64_1693` `not-gt_binary64_1692` `not-lt_binary64_1691` `gte-same_binary64_1690` `lte-same_binary64_1689` `gt-same_binary64_1688` `lt-same_binary64_1687` `sinh---cosh_binary64_1634` `sinh-+-cosh_binary64_1633` `sinh-cosh_binary64_1632` `tanh-def-c_binary64_1631` `tanh-def-b_binary64_1630` `tanh-def-a_binary64_1629` `cosh-def_binary64_1628` `sinh-def_binary64_1627` `tan-neg_binary64_1574` `cos-neg_binary64_1573` `sin-neg_binary64_1572` `tan-0_binary64_1571` `cos-0_binary64_1570` `sin-0_binary64_1569` `hang-m-tan_binary64_1568` `hang-p-tan_binary64_1567` `hang-m0-tan_binary64_1566` `hang-p0-tan_binary64_1565` `hang-0m-tan_binary64_1564` `hang-0p-tan_binary64_1563` `tan-+PI/2_binary64_1562` `tan-+PI_binary64_1561` `tan-PI_binary64_1560` `tan-PI/3_binary64_1559` `tan-PI/4_binary64_1558` `tan-PI/6_binary64_1557` `cos-+PI/2_binary64_1556` `cos-+PI_binary64_1555` `cos-PI_binary64_1554` `cos-PI/2_binary64_1553` `cos-PI/3_binary64_1552` `cos-PI/4_binary64_1551` `cos-PI/6_binary64_1550` `sin-+PI/2_binary64_1549` `sin-+PI_binary64_1548` `sin-PI_binary64_1547` `sin-PI/2_binary64_1546` `sin-PI/3_binary64_1545` `sin-PI/4_binary64_1544` `sin-PI/6_binary64_1543` `sub-1-sin_binary64_1542` `sub-1-cos_binary64_1541` `-1-add-sin_binary64_1540` `-1-add-cos_binary64_1539` `1-sub-sin_binary64_1538` `1-sub-cos_binary64_1537` `cos-sin-sum_binary64_1536` `log-E_binary64_1532` `log-rec_binary64_1530` `log-div_binary64_1529` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `div-exp_binary64_1493` `rec-exp_binary64_1492` `prod-exp_binary64_1491` `exp-diff_binary64_1490` `exp-neg_binary64_1489` `exp-sum_binary64_1488` `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` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `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` `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-rgt1-in_binary64_1398` `distribute-lft1-in_binary64_1397` `distribute-rgt-out--_binary64_1396` `distribute-lft-out--_binary64_1394` `associate-/r_binary64_1386` `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

103 → 156

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	3028
1	194	2746
2	550	2734
3	2072	2734
4	3801	2731
5	5166	2731

prune184.0ms (0.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	156	15	171

Error

1.8b

Counts

171 → 15

Compiler

Compiled 5711 to 1200 computations (79% saved)

regimes4.1s (17.2%)

Accuracy

Total 0.4b remaining (9.9%)

Threshold costs 0.4b (9.9%)

Compiler

Compiled 58319 to 35629 computations (38.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

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	26	48
1	34	48
2	34	48

end0.0ms (0%)

sample10.8s (45.1%)

Algorithm

1×

intervals

Results

4.9s	5569×	body	1024	valid
773.0ms	1428×	body	512	valid
421.0ms	211×	body	2048	valid
203.0ms	497×	body	256	valid
50.0ms	295×	body	128	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 5358 to 3305 computations (38.3% 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

analyze2.9s (11.9%)

sample221.0ms (0.9%)

simplify109.0ms (0.5%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite101.0ms (0.4%)

series844.0ms (3.5%)

simplify151.0ms (0.6%)

prune198.0ms (0.8%)

localize25.0ms (0.1%)

rewrite144.0ms (0.6%)

series1.4s (5.8%)

simplify173.0ms (0.7%)

prune255.0ms (1.1%)

localize31.0ms (0.1%)

rewrite127.0ms (0.5%)

series861.0ms (3.6%)

simplify179.0ms (0.7%)

prune247.0ms (1%)

localize31.0ms (0.1%)

rewrite127.0ms (0.5%)

series596.0ms (2.5%)

simplify141.0ms (0.6%)

prune184.0ms (0.8%)

regimes4.1s (17.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample10.8s (45.1%)

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