Details

analyze3.9s (13%)

Algorithm

1×	search
2×	egg-herbie

Rules

966×	`distribute-rgt-in_binary64_1733`
910×	`unsub-neg_binary64_1777`
843×	`distribute-lft-in_binary64_1732`
580×	`distribute-rgt-neg-out_binary64_1743`
450×	`distribute-lft-neg-out_binary64_1742`
437×	`neg-sub0_binary64_1778`
376×	`neg-mul-1_binary64_1779`
344×	`distribute-rgt-neg-in_binary64_1741`
295×	`sub-neg_binary64_1776`
276×	`*-commutative_binary64_1714`
230×	`cancel-sign-sub-inv_binary64_1749`
180×	`distribute-neg-out_binary64_1745`
165×	`distribute-lft-neg-in_binary64_1740`
160×	`associate-l_binary64_1724` `associate-r_binary64_1723` `associate--r+_binary64_1719`
137×	`remove-double-neg_binary64_1771`
130×	`distribute-neg-in_binary64_1744`
113×	`+-commutative_binary64_1713`
100×	`associate-+l-_binary64_1718`
73×	`*-lft-identity_binary64_1772`
67×	`mul0-rgt_binary64_1766` `mul0-lft_binary64_1765`
60×	`+-lft-identity_binary64_1767`
55×	`sub0-neg_binary64_1770`
51×	`*-rgt-identity_binary64_1773`
50×	`associate--r-_binary64_1722`
30×	`distribute-lft-out_binary64_1734`
25×	`--rgt-identity_binary64_1769`
20×	`cancel-sign-sub_binary64_1748` `associate--l+_binary64_1720`
10×	`associate-+r-_binary64_1717` `associate-+l+_binary64_1716` `associate-+r+_binary64_1715`
6×	`distribute-rgt-out--_binary64_1737`
5×	`+-rgt-identity_binary64_1768`
4×	`distribute-lft-out--_binary64_1735`
1×	`1-exp_binary64_1827`
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_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `cos-neg_binary64_1914` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-pow_binary64_1872` `log-rec_binary64_1871` `log-div_binary64_1870` `log-prod_binary64_1869` `pow-base-0_binary64_1867` `unpow1/3_binary64_1850` `unpow3_binary64_1849` `unpow2_binary64_1848` `unpow1/2_binary64_1847` `pow-plus_binary64_1846` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow1_binary64_1841` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-lft-sqr_binary64_1838` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `exp-prod_binary64_1835` `div-exp_binary64_1834` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `exp-diff_binary64_1831` `exp-neg_binary64_1830` `exp-sum_binary64_1829` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-unmult_binary64_1820` `cube-mult_binary64_1813` `cube-div_binary64_1812` `cube-prod_binary64_1811` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `rem-sqrt-square_binary64_1796` `rem-square-sqrt_binary64_1795` `times-frac_binary64_1789` `div-sub_binary64_1788` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `div0_binary64_1764` `-inverses_binary64_1763` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `pow-sqr_binary64_1756` `sqr-pow_binary64_1755` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `difference-of-squares_binary64_1752` `unswap-sqr_binary64_1751` `swap-sqr_binary64_1750` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `distribute-rgt-out_binary64_1736` `count-2_binary64_1731` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `associate-/l_binary64_1728` `associate-/r_binary64_1727` `associate-l/_binary64_1726` `associate-*r/_binary64_1725` `associate--l-_binary64_1721`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	131	605
1	263	605
2	417	605
3	512	605
4	598	605
5	1028	605
6	994	605
7	1659	605
8	2449	605
9	2458	605
10	2534	605
11	2537	605
12	2537	605
13	2903	605
14	2948	605
15	2948	605
16	4374	605
17	4909	605
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
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample222.0ms (0.7%)

Algorithm

1×

intervals

Results

141.0ms	118×	body	1024	valid
39.0ms	55×	body	512	valid
14.0ms	69×	body	128	valid
6.0ms	14×	body	256	valid

Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify56.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

103×	`unsub-neg_binary64_1777`
90×	`associate-l_binary64_1724`
88×	`distribute-rgt-in_binary64_1733`
82×	`cancel-sign-sub-inv_binary64_1749`
80×	`associate-r_binary64_1723`
70×	`distribute-rgt-neg-in_binary64_1741`
58×	`distribute-lft-neg-out_binary64_1742`
57×	`distribute-lft-in_binary64_1732`
56×	`distribute-rgt-neg-out_binary64_1743`
49×	`sub-neg_binary64_1776`
41×	`neg-sub0_binary64_1778`
40×	`distribute-lft-neg-in_binary64_1740`
34×	`neg-mul-1_binary64_1779`
33×	`associate--r+_binary64_1719`
28×	`*-commutative_binary64_1714`
25×	`distribute-neg-in_binary64_1744`
21×	`mul0-rgt_binary64_1766` `mul0-lft_binary64_1765`
17×	`+-commutative_binary64_1713`
14×	`associate-+l-_binary64_1718`
13×	`*-lft-identity_binary64_1772`
12×	`remove-double-neg_binary64_1771`
8×	`sub0-neg_binary64_1770` `+-lft-identity_binary64_1767`
7×	`*-rgt-identity_binary64_1773`
5×	`associate--l+_binary64_1720` `associate-+l+_binary64_1716`
4×	`mul-1-neg_binary64_1775`
3×	`--rgt-identity_binary64_1769` `associate--r-_binary64_1722` `associate--l-_binary64_1721` `associate-+r+_binary64_1715`
2×	`+-rgt-identity_binary64_1768`
1×	`1-exp_binary64_1827` `cancel-sign-sub_binary64_1748` `associate-+r-_binary64_1717`
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_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `cos-neg_binary64_1914` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-pow_binary64_1872` `log-rec_binary64_1871` `log-div_binary64_1870` `log-prod_binary64_1869` `pow-base-0_binary64_1867` `unpow1/3_binary64_1850` `unpow3_binary64_1849` `unpow2_binary64_1848` `unpow1/2_binary64_1847` `pow-plus_binary64_1846` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow1_binary64_1841` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-lft-sqr_binary64_1838` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `exp-prod_binary64_1835` `div-exp_binary64_1834` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `exp-diff_binary64_1831` `exp-neg_binary64_1830` `exp-sum_binary64_1829` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-unmult_binary64_1820` `cube-mult_binary64_1813` `cube-div_binary64_1812` `cube-prod_binary64_1811` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `rem-sqrt-square_binary64_1796` `rem-square-sqrt_binary64_1795` `times-frac_binary64_1789` `div-sub_binary64_1788` `/-rgt-identity_binary64_1774` `div0_binary64_1764` `-inverses_binary64_1763` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `pow-sqr_binary64_1756` `sqr-pow_binary64_1755` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `difference-of-squares_binary64_1752` `unswap-sqr_binary64_1751` `swap-sqr_binary64_1750` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `distribute-rgt-out--_binary64_1737` `distribute-rgt-out_binary64_1736` `distribute-lft-out--_binary64_1735` `distribute-lft-out_binary64_1734` `count-2_binary64_1731` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `associate-/l_binary64_1728` `associate-/r_binary64_1727` `associate-l/_binary64_1726` `associate-*r/_binary64_1725`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.2b

Counts

2 → 1

Compiler

Compiled 66 to 46 computations (30.3% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.7b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite154.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

12×	`add-sqr-sqrt_binary64_1805`
8×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`add-log-exp_binary64_1822` `associate-l_binary64_1724` `associate-r_binary64_1723`
2×	`sin-mult_binary64_1938` `pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714`
1×	`diff-log_binary64_1875` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `cancel-sign-sub-inv_binary64_1749` `asin-acos_binary64_1963`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
6.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
4.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 2653 to 371 computations (86% saved)

series1.6s (5.3%)

Error

0.2b

Counts

4 → 45

Calls

4 calls:

657.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
559.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
178.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
109.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 4358 to 2057 computations (52.8% saved)

simplify149.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

616×	`sub-neg_binary64_1776`
326×	`distribute-rgt-neg-in_binary64_1741`
291×	`distribute-lft-neg-in_binary64_1740`
284×	`*-commutative_binary64_1714`
275×	`unsub-neg_binary64_1777`
269×	`cancel-sign-sub-inv_binary64_1749`
212×	`associate-+l-_binary64_1718`
205×	`associate-+l+_binary64_1716`
193×	`neg-mul-1_binary64_1779`
176×	`associate-+r+_binary64_1715`
172×	`neg-sub0_binary64_1778`
161×	`distribute-rgt-in_binary64_1733`
145×	`+-commutative_binary64_1713`
136×	`associate--l+_binary64_1720`
130×	`associate-l_binary64_1724`
125×	`associate-r_binary64_1723`
120×	`distribute-lft-in_binary64_1732`
93×	`sqr-pow_binary64_1755`
81×	`associate--r+_binary64_1719` `associate-+r-_binary64_1717`
74×	`distribute-lft-out_binary64_1734`
51×	`distribute-lft-out--_binary64_1735`
43×	`exp-prod_binary64_1835` `unswap-sqr_binary64_1751`
42×	`distribute-rgt-out_binary64_1736`
34×	`associate--l-_binary64_1721`
33×	`distribute-rgt-out--_binary64_1737`
28×	`distribute-lft-neg-out_binary64_1742`
24×	`sub0-neg_binary64_1770` `swap-sqr_binary64_1750`
23×	`+-rgt-identity_binary64_1768`
20×	`cube-prod_binary64_1811` `distribute-neg-in_binary64_1744`
19×	`log-prod_binary64_1869`
18×	`exp-sum_binary64_1829` `*-lft-identity_binary64_1772`
16×	`times-frac_binary64_1789` `*-rgt-identity_binary64_1773`
13×	`distribute-rgt-neg-out_binary64_1743`
12×	`cube-unmult_binary64_1820`
10×	`unpow3_binary64_1849` `exp-diff_binary64_1831` `difference-of-squares_binary64_1752`
9×	`pow-sqr_binary64_1756`
6×	`unpow1/2_binary64_1847` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `associate-/r*_binary64_1727`
5×	`pow-plus_binary64_1846` `cube-mult_binary64_1813` `rem-sqrt-square_binary64_1796` `div-sub_binary64_1788` `associate--r-_binary64_1722`
4×	`sqr-neg_binary64_1797` `cancel-sign-sub_binary64_1748` `associate-/l*_binary64_1728`
2×	`cos-neg_binary64_1914` `distribute-rgt1-in_binary64_1739` `associate-/l/_binary64_1730` `associate-*r/_binary64_1725`
1×	`unpow2_binary64_1848` `unpow1_binary64_1841` `div-exp_binary64_1834` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `cube-neg_binary64_1810` `distribute-lft1-in_binary64_1738` `count-2_binary64_1731`
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_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-pow_binary64_1872` `log-rec_binary64_1871` `log-div_binary64_1870` `pow-base-0_binary64_1867` `unpow1/3_binary64_1850` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-lft-sqr_binary64_1838` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `exp-neg_binary64_1830` `e-exp-1_binary64_1828` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-div_binary64_1812` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `rem-square-sqrt_binary64_1795` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `+-lft-identity_binary64_1767` `div0_binary64_1764` `-inverses_binary64_1763` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `associate-/r/_binary64_1729` `associate-l/_binary64_1726`

Counts

103 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	184	3379
1	425	3199
2	1134	3111
3	2158	3101
4	4259	3101
5	5039	3101

prune178.0ms (0.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	68	11	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	11	80

Error

0.1b

Counts

80 → 11

Compiler

Compiled 3837 to 726 computations (81.1% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.5b	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))

rewrite173.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

6×	`add-log-exp_binary64_1822` `sin-mult_binary64_1938`
5×	`cos-mult_binary64_1937`
4×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
3×	`frac-sub_binary64_1792` `asin-acos_binary64_1963`
2×	`associate-l/_binary64_1726` `associate-r/_binary64_1725` `sub-div_binary64_1790`
1×	`diff-log_binary64_1875` `frac-times_binary64_1793` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `difference-of-squares_binary64_1752` `cancel-sign-sub-inv_binary64_1749` `sqr-cos-a_binary64_1932` `associate--l+_binary64_1720`

Counts

4 → 43

Calls

4 calls:

10.0ms	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 4337 to 355 computations (91.8% saved)

series1.7s (5.8%)

Error

0.1b

Counts

4 → 40

Calls

4 calls:

1.2s	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
143.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
139.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
132.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 8517 to 2336 computations (72.6% saved)

simplify160.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

464×	`cancel-sign-sub-inv_binary64_1749`
409×	`unswap-sqr_binary64_1751`
364×	`neg-mul-1_binary64_1779`
315×	`distribute-rgt-neg-in_binary64_1741`
294×	`distribute-lft-neg-in_binary64_1740`
241×	`*-commutative_binary64_1714`
183×	`exp-prod_binary64_1835`
182×	`sub-neg_binary64_1776`
162×	`distribute-rgt-in_binary64_1733`
151×	`distribute-lft-in_binary64_1732`
115×	`times-frac_binary64_1789`
113×	`neg-sub0_binary64_1778`
110×	`sqr-pow_binary64_1755`
109×	`unsub-neg_binary64_1777`
108×	`distribute-lft-neg-out_binary64_1742`
94×	`distribute-rgt-neg-out_binary64_1743`
87×	`associate-r_binary64_1723`
74×	`cube-prod_binary64_1811`
70×	`associate-l_binary64_1724`
62×	`distribute-neg-in_binary64_1744`
57×	`+-commutative_binary64_1713`
54×	`swap-sqr_binary64_1750`
52×	`associate--r+_binary64_1719`
51×	`distribute-rgt-out_binary64_1736`
46×	`exp-sum_binary64_1829`
36×	`associate--l+_binary64_1720`
35×	`associate-+l+_binary64_1716`
34×	`associate-+r+_binary64_1715`
33×	`difference-of-squares_binary64_1752`
27×	`unpow3_binary64_1849` `associate-/l*_binary64_1728` `associate-+l-_binary64_1718`
22×	`pow-sqr_binary64_1756`
20×	`associate-+r-_binary64_1717`
19×	`exp-diff_binary64_1831`
17×	`+-rgt-identity_binary64_1768` `associate-/r*_binary64_1727`
16×	`cube-unmult_binary64_1820` `sub0-neg_binary64_1770`
15×	`cube-mult_binary64_1813`
14×	`mul0-rgt_binary64_1766` `mul0-lft_binary64_1765`
13×	`sqr-neg_binary64_1797` `remove-double-neg_binary64_1771`
12×	`pow-plus_binary64_1846`
11×	`div-sub_binary64_1788`
10×	`distribute-lft-out_binary64_1734`
7×	`associate--r-_binary64_1722`
6×	`unpow2_binary64_1848` `associate-*r/_binary64_1725`
5×	`unpow1/2_binary64_1847` `unpow1_binary64_1841` `rem-sqrt-square_binary64_1796` `associate-/l/_binary64_1730`
4×	`log-prod_binary64_1869` `distribute-neg-out_binary64_1745` `associate-/r/_binary64_1729`
3×	`exp-neg_binary64_1830` `distribute-rgt-out--_binary64_1737`
2×	`cube-neg_binary64_1810` `cancel-sign-sub_binary64_1748` `count-2_binary64_1731` `associate--l-_binary64_1721`
1×	`cos-neg_binary64_1914` `cos-0_binary64_1911` `div-exp_binary64_1834` `1-exp_binary64_1827` `+-inverses_binary64_1762` `difference-of-sqr-1_binary64_1753` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate-*l/_binary64_1726`
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_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `sin-neg_binary64_1913` `tan-0_binary64_1912` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-pow_binary64_1872` `log-rec_binary64_1871` `log-div_binary64_1870` `pow-base-0_binary64_1867` `unpow1/3_binary64_1850` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-lft-sqr_binary64_1838` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-div_binary64_1812` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `rem-square-sqrt_binary64_1795` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `-rgt-identity_binary64_1773` `-lft-identity_binary64_1772` `--rgt-identity_binary64_1769` `+-lft-identity_binary64_1767` `div0_binary64_1764` `*-inverses_binary64_1763` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-lft-out--_binary64_1735`

Counts

83 → 31

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	113	3777
1	281	3481
2	871	3444
3	2292	3444
4	4535	3369
5	5065	3369

prune127.0ms (0.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	31	11	42

Error

0.1b

Counts

42 → 11

Compiler

Compiled 2977 to 644 computations (78.4% saved)

localize44.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.4b	(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3))
0.5b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)

rewrite288.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

16×	`add-sqr-sqrt_binary64_1805`
8×	`*-un-lft-identity_binary64_1783` `sqr-pow_binary64_1755` `difference-of-squares_binary64_1752` `cancel-sign-sub-inv_binary64_1749`
7×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
6×	`add-cube-cbrt_binary64_1818` `add-log-exp_binary64_1822`
4×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
3×	`pow-unpow_binary64_1860`
2×	`pow-pow_binary64_1855` `pow-exp_binary64_1851` `unpow3_binary64_1849` `cube-mult_binary64_1813` `rem-cube-cbrt_binary64_1806` `asin-acos_binary64_1963`
1×	`pow-prod-down_binary64_1854` `pow-to-exp_binary64_1852` `prod-exp_binary64_1832` `sin-mult_binary64_1938` `cube-div_binary64_1812` `cbrt-unprod_binary64_1816` `diff-log_binary64_1875` `flip3--_binary64_1787` `difference-cubes_binary64_1785` `sub-neg_binary64_1776` `flip--_binary64_1758` `distribute-lft-out--_binary64_1735`

Counts

4 → 68

Calls

4 calls:

11.0ms	(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3))
6.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 7202 to 951 computations (86.8% saved)

series3.0s (10.1%)

Error

0.1b

Counts

4 → 41

Calls

4 calls:

1.5s	(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3))
1.1s	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
151.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
145.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 10305 to 3130 computations (69.6% saved)

simplify195.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

458×	`exp-prod_binary64_1835`
376×	`distribute-rgt-neg-in_binary64_1741`
336×	`cancel-sign-sub-inv_binary64_1749`
333×	`*-commutative_binary64_1714`
225×	`sqr-pow_binary64_1755`
186×	`sub-neg_binary64_1776`
182×	`unswap-sqr_binary64_1751`
174×	`log-prod_binary64_1869`
173×	`swap-sqr_binary64_1750`
138×	`cube-prod_binary64_1811`
118×	`distribute-lft-neg-in_binary64_1740`
111×	`associate-l_binary64_1724`
110×	`difference-of-squares_binary64_1752` `associate-r_binary64_1723`
108×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
88×	`distribute-rgt-in_binary64_1733`
86×	`unsub-neg_binary64_1777`
83×	`distribute-lft-in_binary64_1732`
77×	`unpow3_binary64_1849`
68×	`+-commutative_binary64_1713`
67×	`distribute-lft-neg-out_binary64_1742`
60×	`exp-sum_binary64_1829`
44×	`distribute-rgt-neg-out_binary64_1743`
38×	`pow-sqr_binary64_1756`
37×	`distribute-rgt-out_binary64_1736`
35×	`associate-+l+_binary64_1716`
34×	`associate--r+_binary64_1719`
33×	`cube-mult_binary64_1813`
30×	`pow-plus_binary64_1846` `associate-+l-_binary64_1718`
26×	`distribute-lft-out_binary64_1734`
25×	`log-pow_binary64_1872`
24×	`associate-+r+_binary64_1715`
22×	`associate--l+_binary64_1720`
20×	`sub0-neg_binary64_1770` `associate-+r-_binary64_1717`
17×	`mul0-rgt_binary64_1766` `mul0-lft_binary64_1765`
15×	`times-frac_binary64_1789` `+-rgt-identity_binary64_1768`
14×	`cube-unmult_binary64_1820` `distribute-neg-in_binary64_1744`
12×	`exp-diff_binary64_1831`
11×	`exp-neg_binary64_1830`
9×	`rem-sqrt-square_binary64_1796`
3×	`-rgt-identity_binary64_1773` `-lft-identity_binary64_1772` `difference-of-sqr-1_binary64_1753` `cancel-sign-sub_binary64_1748` `associate-/l/_binary64_1730` `associate-*r/_binary64_1725` `associate--l-_binary64_1721`
2×	`unpow2_binary64_1848` `unpow1/2_binary64_1847` `unpow1_binary64_1841` `sqr-neg_binary64_1797` `rem-square-sqrt_binary64_1795` `distribute-rgt-out--_binary64_1737` `distribute-lft-out--_binary64_1735` `count-2_binary64_1731`
1×	`cos-neg_binary64_1914` `div-exp_binary64_1834` `1-exp_binary64_1827` `rem-cbrt-cube_binary64_1807` `distribute-neg-out_binary64_1745` `associate-/r/_binary64_1729` `associate-/l*_binary64_1728`
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_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-rec_binary64_1871` `log-div_binary64_1870` `pow-base-0_binary64_1867` `unpow1/3_binary64_1850` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-lft-sqr_binary64_1838` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-div_binary64_1812` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `div-sub_binary64_1788` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `+-lft-identity_binary64_1767` `div0_binary64_1764` `-inverses_binary64_1763` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate-/r_binary64_1727` `associate-*l/_binary64_1726` `associate--r-_binary64_1722`

Counts

109 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	150	4788
1	342	4506
2	1094	4472
3	2659	4472
4	4766	4463
5	4935	4463

prune223.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	1	8	9
Picked	1	0	1
Done	1	0	1
Total	57	10	67

Error

0.1b

Counts

67 → 10

Compiler

Compiled 6015 to 926 computations (84.6% saved)

localize49.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.4b	(-.f64 (pow.f64 (cos.f64 delta) 3) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 9)))
0.8b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 9)
6.1b	(cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 9))

rewrite310.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

25×	`add-sqr-sqrt_binary64_1805`
18×	`cbrt-prod_binary64_1814`
12×	`difference-of-squares_binary64_1752`
10×	`*-un-lft-identity_binary64_1783` `sqr-pow_binary64_1755`
8×	`add-cube-cbrt_binary64_1818` `cancel-sign-sub-inv_binary64_1749`
7×	`pow1_binary64_1844` `add-exp-log_binary64_1821`
6×	`add-log-exp_binary64_1822` `unpow-prod-down_binary64_1862`
4×	`add-cbrt-cube_binary64_1819`
3×	`pow-unpow_binary64_1860` `cube-prod_binary64_1811`
2×	`pow-pow_binary64_1855` `pow-exp_binary64_1851`
1×	`pow1/3_binary64_1865` `pow-prod-down_binary64_1854` `pow-to-exp_binary64_1852` `prod-exp_binary64_1832` `diff-log_binary64_1875` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `distribute-lft-out--_binary64_1735` `asin-acos_binary64_1963`

Counts

4 → 70

Calls

4 calls:

11.0ms	(-.f64 (pow.f64 (cos.f64 delta) 3) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 9)))
6.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 9)
3.0ms	(cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 9))
2.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 7492 to 1140 computations (84.8% saved)

series4.9s (16.4%)

Error

0.1b

Counts

4 → 42

Calls

4 calls:

2.0s	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 9)
1.5s	(-.f64 (pow.f64 (cos.f64 delta) 3) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 9)))
1.2s	(cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 9))
143.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 10686 to 3346 computations (68.7% saved)

simplify187.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

692×	`associate-l_binary64_1724`
656×	`associate-r_binary64_1723`
526×	`distribute-rgt-neg-in_binary64_1741`
266×	`cancel-sign-sub-inv_binary64_1749`
203×	`sub-neg_binary64_1776`
189×	`*-commutative_binary64_1714`
153×	`unswap-sqr_binary64_1751`
141×	`sqr-pow_binary64_1755`
120×	`distribute-lft-neg-in_binary64_1740`
112×	`distribute-lft-neg-out_binary64_1742`
104×	`neg-sub0_binary64_1778`
97×	`neg-mul-1_binary64_1779`
85×	`exp-prod_binary64_1835`
82×	`distribute-rgt-neg-out_binary64_1743`
75×	`swap-sqr_binary64_1750`
68×	`+-commutative_binary64_1713`
59×	`cube-prod_binary64_1811`
55×	`unsub-neg_binary64_1777`
53×	`log-prod_binary64_1869`
50×	`difference-of-squares_binary64_1752`
48×	`distribute-rgt-in_binary64_1733`
43×	`distribute-lft-in_binary64_1732`
34×	`cube-unmult_binary64_1820` `associate--r+_binary64_1719`
32×	`associate-+l-_binary64_1718`
31×	`associate-+l+_binary64_1716`
29×	`pow-plus_binary64_1846`
26×	`pow-sqr_binary64_1756`
22×	`sub0-neg_binary64_1770` `associate--l+_binary64_1720`
21×	`associate-+r-_binary64_1717`
18×	`unpow3_binary64_1849` `exp-sum_binary64_1829`
15×	`distribute-rgt-out_binary64_1736` `associate-+r+_binary64_1715`
14×	`distribute-neg-in_binary64_1744`
13×	`+-rgt-identity_binary64_1768`
11×	`log-pow_binary64_1872` `cube-mult_binary64_1813` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765`
9×	`rem-sqrt-square_binary64_1796`
8×	`distribute-lft-out_binary64_1734`
6×	`exp-diff_binary64_1831`
3×	`mul-1-neg_binary64_1775` `-rgt-identity_binary64_1773` `-lft-identity_binary64_1772` `cancel-sign-sub_binary64_1748` `distribute-rgt-out--_binary64_1737` `distribute-lft-out--_binary64_1735` `count-2_binary64_1731` `associate--l-_binary64_1721`
2×	`unpow1/2_binary64_1847` `unpow1_binary64_1841` `rem-3cbrt-lft_binary64_1808` `rem-square-sqrt_binary64_1795` `difference-of-sqr-1_binary64_1753` `associate-/l/_binary64_1730` `associate-*r/_binary64_1725`
1×	`unpow2_binary64_1848` `div-exp_binary64_1834` `1-exp_binary64_1827` `sqr-neg_binary64_1797` `distribute-neg-out_binary64_1745` `associate-/r/_binary64_1729` `associate-/l*_binary64_1728`
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_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `cos-neg_binary64_1914` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-rec_binary64_1871` `log-div_binary64_1870` `pow-base-0_binary64_1867` `unpow1/3_binary64_1850` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-lft-sqr_binary64_1838` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `exp-neg_binary64_1830` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-div_binary64_1812` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `times-frac_binary64_1789` `div-sub_binary64_1788` `/-rgt-identity_binary64_1774` `remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `+-lft-identity_binary64_1767` `div0_binary64_1764` `-inverses_binary64_1763` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate-/r_binary64_1727` `associate-*l/_binary64_1726` `associate--r-_binary64_1722`

Counts

112 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	5714
1	390	5538
2	1026	5474
3	3702	5338
4	4994	5338

prune207.0ms (0.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	60	10	70

Error

0.1b

Counts

70 → 10

Compiler

Compiled 5908 to 797 computations (86.5% saved)

regimes2.1s (7.1%)

Accuracy

Total 0.1b remaining (69.9%)

Threshold costs 0.1b (69.9%)

Compiler

Compiled 32667 to 15008 computations (54.1% saved)

bsearch0.0ms (0%)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64_1714`
6×	`+-commutative_binary64_1713`
2×	`sub-neg_binary64_1776`
1×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
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_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `unpow1_binary64_1841` `e-exp-1_binary64_1828` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `unsub-neg_binary64_1777` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `-rgt-identity_binary64_1773` `-lft-identity_binary64_1772` `remove-double-neg_binary64_1771` `sub0-neg_binary64_1770` `--rgt-identity_binary64_1769` `+-rgt-identity_binary64_1768` `+-lft-identity_binary64_1767` `cancel-sign-sub-inv_binary64_1749` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-neg-in_binary64_1744` `distribute-rgt-neg-out_binary64_1743` `distribute-lft-neg-out_binary64_1742` `distribute-rgt-neg-in_binary64_1741` `distribute-lft-neg-in_binary64_1740`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	146
1	48	146
2	53	146
3	55	146
4	56	146
5	56	146

end0.0ms (0%)

sample9.8s (32.9%)

Algorithm

1×

intervals

Results

4.9s	3899×	body	1024	valid
977.0ms	1323×	body	512	valid
464.0ms	2190×	body	128	valid
273.0ms	582×	body	256	valid
15.0ms	6×	body	2048	valid

Compiler

Compiled 4768 to 2187 computations (54.1% saved)

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

Details

analyze3.9s (13%)

sample222.0ms (0.7%)

simplify56.0ms (0.2%)

prune5.0ms (0%)

localize27.0ms (0.1%)

rewrite154.0ms (0.5%)

series1.6s (5.3%)

simplify149.0ms (0.5%)

prune178.0ms (0.6%)

localize40.0ms (0.1%)

rewrite173.0ms (0.6%)

series1.7s (5.8%)

simplify160.0ms (0.5%)

prune127.0ms (0.4%)

localize44.0ms (0.1%)

rewrite288.0ms (1%)

series3.0s (10.1%)

simplify195.0ms (0.7%)

prune223.0ms (0.7%)

localize49.0ms (0.2%)

rewrite310.0ms (1%)

series4.9s (16.4%)

simplify187.0ms (0.6%)

prune207.0ms (0.7%)

regimes2.1s (7.1%)

bsearch0.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample9.8s (32.9%)

Profiling

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55