Details

analyze4.0s (16.8%)

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)

sample232.0ms (1%)

Algorithm

1×

intervals

Results

150.0ms	129×	body	1024	valid
33.0ms	39×	body	512	valid
21.0ms	80×	body	128	valid
3.0ms	7×	body	256	valid
3.0ms	1×	body	2048	valid

Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify47.0ms (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:

0.1b	(.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))
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))))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.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 (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

11×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
9×	`add-sqr-sqrt_binary64_1805`
7×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`add-log-exp_binary64_1822` `associate-r_binary64_1723`
4×	`pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `associate-l_binary64_1724`
2×	`*-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` `sin-mult_binary64_1938` `unswap-sqr_binary64_1751`

Counts

4 → 57

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))
7.0ms	(.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))))))
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 2634 to 438 computations (83.4% saved)

series1.7s (7.1%)

Error

0.2b

Counts

4 → 42

Calls

4 calls:

640.0ms	(-.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)))))))
550.0ms	(.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))))))
355.0ms	(.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))
107.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 4192 to 1991 computations (52.5% saved)

simplify171.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

470×	`distribute-rgt-in_binary64_1733`
384×	`distribute-rgt-neg-in_binary64_1741`
362×	`*-commutative_binary64_1714`
354×	`distribute-lft-in_binary64_1732`
341×	`distribute-lft-neg-in_binary64_1740`
297×	`cancel-sign-sub-inv_binary64_1749`
268×	`neg-mul-1_binary64_1779`
195×	`sub-neg_binary64_1776`
191×	`unsub-neg_binary64_1777`
180×	`associate-l_binary64_1724`
175×	`sqr-pow_binary64_1755`
146×	`associate-r_binary64_1723`
135×	`neg-sub0_binary64_1778`
105×	`unswap-sqr_binary64_1751`
94×	`times-frac_binary64_1789`
67×	`associate-+l+_binary64_1716`
66×	`exp-prod_binary64_1835` `associate-+r+_binary64_1715`
64×	`distribute-neg-in_binary64_1744`
59×	`distribute-lft-neg-out_binary64_1742`
58×	`+-commutative_binary64_1713`
50×	`distribute-rgt-out_binary64_1736`
48×	`distribute-rgt-neg-out_binary64_1743`
43×	`cube-prod_binary64_1811` `pow-sqr_binary64_1756` `distribute-neg-out_binary64_1745`
41×	`rem-sqrt-square_binary64_1796`
38×	`exp-sum_binary64_1829`
34×	`log-prod_binary64_1869`
32×	`swap-sqr_binary64_1750` `associate-+l-_binary64_1718`
30×	`distribute-rgt-out--_binary64_1737`
27×	`sub0-neg_binary64_1770`
24×	`mul0-rgt_binary64_1766` `mul0-lft_binary64_1765`
20×	`associate-+r-_binary64_1717`
19×	`cube-unmult_binary64_1820` `+-rgt-identity_binary64_1768`
18×	`difference-of-squares_binary64_1752`
16×	`*-lft-identity_binary64_1772`
15×	`unpow3_binary64_1849` `*-rgt-identity_binary64_1773`
14×	`unpow1/2_binary64_1847` `exp-diff_binary64_1831`
10×	`div-sub_binary64_1788` `associate-/l*_binary64_1728` `associate--r+_binary64_1719`
9×	`distribute-lft-out_binary64_1734`
8×	`associate--l+_binary64_1720`
6×	`cube-mult_binary64_1813` `+-lft-identity_binary64_1767` `associate-/r*_binary64_1727`
5×	`remove-double-neg_binary64_1771`
4×	`sqr-neg_binary64_1797` `distribute-rgt1-in_binary64_1739`
3×	`cube-neg_binary64_1810` `--rgt-identity_binary64_1769` `cancel-sign-sub_binary64_1748` `distribute-frac-neg_binary64_1746` `distribute-lft-out--_binary64_1735`
2×	`cos-neg_binary64_1914` `unpow2_binary64_1848` `pow-plus_binary64_1846` `unpow1_binary64_1841` `distribute-lft1-in_binary64_1738` `associate-/l/_binary64_1730` `associate-*r/_binary64_1725`
1×	`sin-neg_binary64_1913` `div-exp_binary64_1834` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `count-2_binary64_1731` `associate--r-_binary64_1722` `associate--l-_binary64_1721`
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` `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` `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` `associate-/r/_binary64_1729` `associate-l/_binary64_1726`

Counts

99 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	148	3281
1	340	3064
2	998	3001
3	1780	3001
4	3087	2999
5	4734	2999
6	4990	2999

prune158.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	9	71

Error

0.1b

Counts

71 → 9

Compiler

Compiled 3364 to 633 computations (81.2% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.5b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))) 3)))))
0.6b	(pow.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))) 3)
7.1b	(cbrt.f64 (pow.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))) 3))

rewrite165.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

12×	`cbrt-prod_binary64_1814`
10×	`add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
6×	`add-log-exp_binary64_1822` `unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
5×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
3×	`pow-unpow_binary64_1860`
2×	`unpow3_binary64_1849` `cube-mult_binary64_1813` `sqr-pow_binary64_1755`
1×	`pow1/3_binary64_1865` `rem-cbrt-cube_binary64_1807` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `rem-cube-cbrt_binary64_1806` `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 → 64

Calls

4 calls:

4.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))) 3)))))
3.0ms	(pow.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))) 3)
3.0ms	(cbrt.f64 (pow.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)))))

Compiler

Compiled 3426 to 786 computations (77.1% saved)

series1.4s (5.9%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

632.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))) 3)))))
504.0ms	(pow.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))) 3)
113.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
108.0ms	(cbrt.f64 (pow.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))) 3))

Compiler

Compiled 3990 to 2058 computations (48.4% saved)

simplify237.0ms (1%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-l_binary64_1724`
426×	`associate-r_binary64_1723`
414×	`log-prod_binary64_1869`
291×	`exp-prod_binary64_1835`
247×	`distribute-rgt-in_binary64_1733`
233×	`unswap-sqr_binary64_1751`
226×	`cube-prod_binary64_1811`
204×	`distribute-lft-in_binary64_1732`
155×	`swap-sqr_binary64_1750`
143×	`sqr-pow_binary64_1755`
134×	`unpow3_binary64_1849`
112×	`cancel-sign-sub-inv_binary64_1749`
89×	`pow-plus_binary64_1846`
85×	`distribute-rgt-neg-in_binary64_1741`
82×	`log-pow_binary64_1872` `distribute-lft-neg-in_binary64_1740`
77×	`associate-+l+_binary64_1716` `*-commutative_binary64_1714`
61×	`associate-/l*_binary64_1728`
54×	`sub-neg_binary64_1776`
46×	`distribute-lft-neg-out_binary64_1742`
41×	`pow-sqr_binary64_1756`
39×	`distribute-rgt-neg-out_binary64_1743`
32×	`distribute-rgt-out_binary64_1736`
31×	`neg-sub0_binary64_1778`
28×	`neg-mul-1_binary64_1779` `unsub-neg_binary64_1777`
26×	`associate-+l-_binary64_1718`
25×	`cube-unmult_binary64_1820`
21×	`+-commutative_binary64_1713`
17×	`distribute-lft-out_binary64_1734`
15×	`cube-mult_binary64_1813`
14×	`associate-+r-_binary64_1717`
13×	`exp-sum_binary64_1829`
12×	`associate-/l/_binary64_1730`
11×	`count-2_binary64_1731`
10×	`rem-sqrt-square_binary64_1796` `difference-of-squares_binary64_1752` `associate-+r+_binary64_1715`
8×	`sub0-neg_binary64_1770` `associate--l+_binary64_1720` `associate--r+_binary64_1719`
7×	`associate-*r/_binary64_1725`
6×	`+-rgt-identity_binary64_1768` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `associate-/r*_binary64_1727`
5×	`exp-diff_binary64_1831`
4×	`unpow2_binary64_1848` `rem-cbrt-cube_binary64_1807` `-rgt-identity_binary64_1773` `-lft-identity_binary64_1772` `distribute-neg-in_binary64_1744`
3×	`mul-1-neg_binary64_1775` `associate-*l/_binary64_1726`
2×	`unpow1/2_binary64_1847` `unpow1_binary64_1841` `distribute-rgt-out--_binary64_1737` `distribute-lft-out--_binary64_1735` `associate-/r/_binary64_1729`
1×	`div-exp_binary64_1834` `1-exp_binary64_1827` `rem-3cbrt-lft_binary64_1808` `rem-cube-cbrt_binary64_1806` `sqr-neg_binary64_1797` `rem-square-sqrt_binary64_1795` `associate--r-_binary64_1722` `associate--l-_binary64_1721`
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` `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` `difference-of-sqr-1_binary64_1753` `cancel-sign-sub_binary64_1748` `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`

Counts

103 → 55

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	107	3966
1	218	3576
2	575	3535
3	2317	3535
4	4792	3535
5	4924	3532
6	4983	3532
7	4871	3532

prune119.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	55	9	64

Error

0.1b

Counts

64 → 9

Compiler

Compiled 2923 to 580 computations (80.2% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.3b	(*.f64 (cos.f64 delta) (cos.f64 delta))
0.4b	(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)
0.4b	(pow.f64 (cos.f64 delta) 3)

rewrite303.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`pow1_binary64_1844`
14×	`add-sqr-sqrt_binary64_1805`
12×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
6×	`pow-unpow_binary64_1860`
4×	`unpow-prod-down_binary64_1862` `add-log-exp_binary64_1822` `cube-prod_binary64_1811`
3×	`pow-pow_binary64_1855` `pow-exp_binary64_1851` `rem-cube-cbrt_binary64_1806` `swap-sqr_binary64_1750` `associate-l_binary64_1724` `associate-r_binary64_1723`
2×	`pow-to-exp_binary64_1852` `unpow3_binary64_1849` `cube-mult_binary64_1813` `sqr-pow_binary64_1755` `pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
1×	`sin-mult_binary64_1938` `cube-div_binary64_1812` `cos-mult_binary64_1937` `sqr-cos-a_binary64_1932` `pow2_binary64_1864` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846` `pow-sqr_binary64_1756` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714` `asin-acos_binary64_1963`

Counts

4 → 81

Calls

4 calls:

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)
5.0ms	(*.f64 (cos.f64 delta) (cos.f64 delta))
3.0ms	(pow.f64 (cos.f64 delta) 3)
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 7686 to 986 computations (87.2% saved)

series1.5s (6.2%)

Error

0.1b

Counts

4 → 26

Calls

4 calls:

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)
143.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
68.0ms	(pow.f64 (cos.f64 delta) 3)
43.0ms	(*.f64 (cos.f64 delta) (cos.f64 delta))

Compiler

Compiled 6684 to 2032 computations (69.6% saved)

simplify119.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

653×	`sqr-pow_binary64_1755`
355×	`*-commutative_binary64_1714`
306×	`log-prod_binary64_1869`
300×	`exp-prod_binary64_1835`
284×	`associate-+l+_binary64_1716`
235×	`cube-prod_binary64_1811`
224×	`associate-+r+_binary64_1715`
222×	`pow-sqr_binary64_1756`
144×	`distribute-rgt-in_binary64_1733`
137×	`distribute-lft-in_binary64_1732`
136×	`swap-sqr_binary64_1750`
122×	`associate-r_binary64_1723`
115×	`associate-l_binary64_1724`
89×	`associate-/l*_binary64_1728`
79×	`unsub-neg_binary64_1777`
69×	`unpow3_binary64_1849`
66×	`cube-mult_binary64_1813` `neg-mul-1_binary64_1779` `distribute-rgt-neg-in_binary64_1741`
64×	`distribute-lft-neg-in_binary64_1740`
62×	`log-pow_binary64_1872` `neg-sub0_binary64_1778`
47×	`pow-plus_binary64_1846`
46×	`sub-neg_binary64_1776`
40×	`cancel-sign-sub-inv_binary64_1749`
38×	`unswap-sqr_binary64_1751`
25×	`count-2_binary64_1731`
24×	`rem-sqrt-square_binary64_1796`
23×	`distribute-rgt-out_binary64_1736`
22×	`*-rgt-identity_binary64_1773`
21×	`*-lft-identity_binary64_1772` `+-commutative_binary64_1713`
17×	`associate-/l/_binary64_1730`
15×	`cube-unmult_binary64_1820`
12×	`distribute-rgt-neg-out_binary64_1743` `distribute-lft-neg-out_binary64_1742` `associate-/r_binary64_1727` `associate-r/_binary64_1725`
11×	`times-frac_binary64_1789`
10×	`distribute-lft-out_binary64_1734`
8×	`mul0-rgt_binary64_1766` `mul0-lft_binary64_1765`
7×	`unpow1/2_binary64_1847` `associate-/r/_binary64_1729`
6×	`unpow2_binary64_1848`
4×	`unpow1_binary64_1841` `sub0-neg_binary64_1770` `associate-+l-_binary64_1718`
3×	`rem-cbrt-cube_binary64_1807` `+-rgt-identity_binary64_1768` `associate-*l/_binary64_1726` `associate-+r-_binary64_1717`
2×	`sqr-neg_binary64_1797` `/-rgt-identity_binary64_1774` `distribute-rgt-out--_binary64_1737`
1×	`cos-neg_binary64_1914` `cos-0_binary64_1911` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `cube-neg_binary64_1810` `rem-cube-cbrt_binary64_1806` `rem-square-sqrt_binary64_1795` `remove-double-neg_binary64_1771` `+-inverses_binary64_1762` `distribute-lft-out--_binary64_1735`
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-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` `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-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` `sqr-abs_binary64_1798` `div-sub_binary64_1788` `mul-1-neg_binary64_1775` `--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` `difference-of-sqr-1_binary64_1753` `difference-of-squares_binary64_1752` `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-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate--r-_binary64_1722` `associate--l-_binary64_1721` `associate--l+_binary64_1720` `associate--r+_binary64_1719`

Counts

107 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	2230
1	254	2011
2	894	1958
3	1835	1958
4	3869	1958
5	5140	1958

prune291.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	83	10	93

Error

0.0b

Counts

93 → 10

Compiler

Compiled 8136 to 1206 computations (85.2% saved)

localize53.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cos.f64 delta) (cos.f64 delta))
0.4b	(pow.f64 (sin.f64 phi1) 3)
0.4b	(pow.f64 (cos.f64 delta) 3)
0.5b	(pow.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 3)

rewrite368.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`add-sqr-sqrt_binary64_1805`
17×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
14×	`pow1_binary64_1844`
9×	`unpow-prod-down_binary64_1862` `pow-unpow_binary64_1860` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `cube-prod_binary64_1811`
4×	`add-log-exp_binary64_1822`
3×	`pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `unpow3_binary64_1849` `cube-mult_binary64_1813` `rem-cube-cbrt_binary64_1806` `sqr-pow_binary64_1755` `swap-sqr_binary64_1750` `associate-l_binary64_1724` `associate-r_binary64_1723`
1×	`cos-mult_binary64_1937` `sqr-cos-a_binary64_1932` `pow2_binary64_1864` `pow-prod-down_binary64_1854` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `pow-sqr_binary64_1756` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714`

Counts

4 → 96

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 delta) (cos.f64 delta))
4.0ms	(pow.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 3)
3.0ms	(pow.f64 (sin.f64 phi1) 3)
3.0ms	(pow.f64 (cos.f64 delta) 3)

Compiler

Compiled 9216 to 1402 computations (84.8% saved)

series1.0s (4.3%)

Error

0.0b

Counts

4 → 20

Calls

4 calls:

768.0ms	(pow.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 3)
77.0ms	(pow.f64 (sin.f64 phi1) 3)
70.0ms	(pow.f64 (cos.f64 delta) 3)
48.0ms	(*.f64 (cos.f64 delta) (cos.f64 delta))

Compiler

Compiled 5118 to 1795 computations (64.9% saved)

simplify111.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

851×	`sqr-pow_binary64_1755`
396×	`log-prod_binary64_1869`
380×	`exp-prod_binary64_1835`
352×	`*-commutative_binary64_1714`
323×	`pow-sqr_binary64_1756`
284×	`cube-prod_binary64_1811`
129×	`swap-sqr_binary64_1750`
123×	`associate-r_binary64_1723`
121×	`distribute-rgt-in_binary64_1733`
120×	`associate-l_binary64_1724`
113×	`log-pow_binary64_1872`
111×	`associate-/l*_binary64_1728`
109×	`distribute-lft-in_binary64_1732`
93×	`unpow3_binary64_1849`
89×	`cube-mult_binary64_1813`
83×	`pow-plus_binary64_1846`
60×	`unswap-sqr_binary64_1751`
40×	`count-2_binary64_1731`
39×	`distribute-rgt-out_binary64_1736`
38×	`rem-sqrt-square_binary64_1796`
30×	`*-rgt-identity_binary64_1773`
29×	`*-lft-identity_binary64_1772`
26×	`+-commutative_binary64_1713`
23×	`associate-+l+_binary64_1716` `associate-+r+_binary64_1715`
18×	`distribute-lft-out_binary64_1734`
17×	`cube-unmult_binary64_1820` `neg-mul-1_binary64_1779` `sub-neg_binary64_1776` `distribute-rgt-neg-in_binary64_1741` `associate-/l/_binary64_1730`
16×	`cancel-sign-sub-inv_binary64_1749`
15×	`neg-sub0_binary64_1778` `distribute-lft-neg-in_binary64_1740`
12×	`unpow2_binary64_1848` `associate-/r_binary64_1727` `associate-r/_binary64_1725`
11×	`times-frac_binary64_1789`
8×	`unpow1/2_binary64_1847`
7×	`associate-/r/_binary64_1729`
5×	`unpow1_binary64_1841`
4×	`rem-cbrt-cube_binary64_1807` `unsub-neg_binary64_1777`
3×	`rem-cube-cbrt_binary64_1806` `rem-square-sqrt_binary64_1795` `associate-*l/_binary64_1726`
2×	`/-rgt-identity_binary64_1774` `sub0-neg_binary64_1770` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `associate-+l-_binary64_1718`
1×	`cos-0_binary64_1911` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `+-rgt-identity_binary64_1768` `+-inverses_binary64_1762` `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` `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` `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-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` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `div-sub_binary64_1788` `mul-1-neg_binary64_1775` `remove-double-neg_binary64_1771` `--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` `difference-of-sqr-1_binary64_1753` `difference-of-squares_binary64_1752` `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-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `distribute-rgt-out--_binary64_1737` `distribute-lft-out--_binary64_1735` `associate--r-_binary64_1722` `associate--l-_binary64_1721` `associate--l+_binary64_1720` `associate--r+_binary64_1719`

Counts

116 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1893
1	264	1678
2	944	1633
3	1994	1633
4	3690	1633
5	5324	1633

prune237.0ms (1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	75	10	85

Error

0.0b

Counts

85 → 10

Compiler

Compiled 6885 to 1023 computations (85.1% saved)

regimes1.8s (7.4%)

Accuracy

Total 0.1b remaining (57.8%)

Threshold costs 0.1b (57.8%)

Compiler

Compiled 26339 to 12936 computations (50.9% saved)

bsearch0.0ms (0%)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64_1714`
9×	`+-commutative_binary64_1713`
4×	`sub-neg_binary64_1776`
3×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
2×	`cancel-sign-sub-inv_binary64_1749` `distribute-rgt-neg-in_binary64_1741`
1×	`distribute-lft-neg-out_binary64_1742` `distribute-lft-neg-in_binary64_1740`
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_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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	145
1	53	145
2	63	145
3	69	145
4	73	145
5	74	145
6	74	145

end0.0ms (0%)

sample9.7s (40.5%)

Algorithm

1×

intervals

Results

5.1s	3992×	body	1024	valid
986.0ms	1329×	body	512	valid
470.0ms	2154×	body	128	valid
255.0ms	511×	body	256	valid
42.0ms	14×	body	2048	valid

Compiler

Compiled 3864 to 1894 computations (51% 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

analyze4.0s (16.8%)

sample232.0ms (1%)

simplify47.0ms (0.2%)

prune5.0ms (0%)

localize27.0ms (0.1%)

rewrite154.0ms (0.6%)

series1.7s (7.1%)

simplify171.0ms (0.7%)

prune158.0ms (0.7%)

localize31.0ms (0.1%)

rewrite165.0ms (0.7%)

series1.4s (5.9%)

simplify237.0ms (1%)

prune119.0ms (0.5%)

localize42.0ms (0.2%)

rewrite303.0ms (1.3%)

series1.5s (6.2%)

simplify119.0ms (0.5%)

prune291.0ms (1.2%)

localize53.0ms (0.2%)

rewrite368.0ms (1.5%)

series1.0s (4.3%)

simplify111.0ms (0.5%)

prune237.0ms (1%)

regimes1.8s (7.4%)

bsearch0.0ms (0%)

simplify8.0ms (0%)

end0.0ms (0%)

sample9.7s (40.5%)

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