Metrics for math.abs on complex

analyze258.0ms (7.3%)

Algorithm

1×	search
2×	egg-herbie

Rules

1× +-commutative_binary64_1713 swap-re-im

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 1-exp_binary64_1827 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 neg-mul-1_binary64_1779 neg-sub0_binary64_1778 unsub-neg_binary64_1777 sub-neg_binary64_1776 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 mul0-rgt_binary64_1766 mul0-lft_binary64_1765 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 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 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 distribute-rgt-in_binary64_1733 distribute-lft-in_binary64_1732 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_1724 associate-*r*_binary64_1723 associate--r-_binary64_1722 associate--l-_binary64_1721 associate--l+_binary64_1720 associate--r+_binary64_1719 associate-+l-_binary64_1718 associate-+r-_binary64_1717 associate-+l+_binary64_1716 associate-+r+_binary64_1715 *-commutative_binary64_1714

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	8	24
2	8	24
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

Symmetry

(sort re im)

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1× +-commutative_binary64_1713

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 1-exp_binary64_1827 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 neg-mul-1_binary64_1779 neg-sub0_binary64_1778 unsub-neg_binary64_1777 sub-neg_binary64_1776 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 mul0-rgt_binary64_1766 mul0-lft_binary64_1765 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 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 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 distribute-rgt-in_binary64_1733 distribute-lft-in_binary64_1732 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_1724 associate-*r*_binary64_1723 associate--r-_binary64_1722 associate--l-_binary64_1721 associate--l+_binary64_1720 associate--r+_binary64_1719 associate-+l-_binary64_1718 associate-+r-_binary64_1717 associate-+l+_binary64_1716 associate-+r+_binary64_1715 *-commutative_binary64_1714

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	8	12
2	8	12

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

31.7b

Counts

1 → 1

Compiler

Compiled 8 to 6 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

29.6b

(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

31.7b

Rules

3×	`add-sqr-sqrt_binary64_1805` `sqrt-prod_binary64_1799`
2×	`pow1_binary64_1844` `add-cube-cbrt_binary64_1818` `sqrt-div_binary64_1800` `*-un-lft-identity_binary64_1783`
1×	`pow1/2_binary64_1863` `add-log-exp_binary64_1822` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `sqrt-pow1_binary64_1801` `flip3-+_binary64_1786` `flip-+_binary64_1757` `rem-sqrt-square_binary64_1796`

Counts

1 → 15

Calls

1 calls:

4.0ms

(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

Compiler

Compiled 264 to 55 computations (79.2% saved)

series75.0ms (2.1%)

Error

0.1b

Counts

1 → 8

Calls

1 calls:

66.0ms

(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

Compiler

Compiled 153 to 133 computations (13.1% saved)

simplify56.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

721×	`unswap-sqr_binary64_1751`
620×	`associate-l_binary64_1724`
563×	`times-frac_binary64_1789`
465×	`associate-/l*_binary64_1728`
236×	`cancel-sign-sub-inv_binary64_1749`
215×	`associate-*l/_binary64_1726`
208×	`associate-/r*_binary64_1727`
162×	`associate-*r/_binary64_1725`
131×	`distribute-rgt-in_binary64_1733`
107×	`distribute-lft-in_binary64_1732`
100×	`associate-/r/_binary64_1729` `associate-r_binary64_1723`
95×	`unsub-neg_binary64_1777`
91×	`neg-sub0_binary64_1778`
89×	`associate-/l/_binary64_1730`
85×	`neg-mul-1_binary64_1779`
79×	`sub-neg_binary64_1776` `distribute-rgt-neg-in_binary64_1741`
78×	`difference-of-squares_binary64_1752`
67×	`distribute-lft-neg-in_binary64_1740`
44×	`sqr-pow_binary64_1755`
39×	`*-commutative_binary64_1714`
38×	`distribute-rgt-out_binary64_1736`
23×	`distribute-lft-neg-out_binary64_1742`
21×	`pow-plus_binary64_1846`
20×	`distribute-rgt-out--_binary64_1737`
19×	`+-commutative_binary64_1713`
18×	`cube-unmult_binary64_1820`
16×	`mul0-rgt_binary64_1766` `mul0-lft_binary64_1765`
15×	`cube-prod_binary64_1811`
11×	`div-sub_binary64_1788` `associate-+l-_binary64_1718` `associate-+r-_binary64_1717`
10×	`+-rgt-identity_binary64_1768` `distribute-rgt-neg-out_binary64_1743`
8×	`distribute-neg-in_binary64_1744`
7×	`distribute-neg-frac_binary64_1747` `distribute-lft-out--_binary64_1735`
6×	`unpow3_binary64_1849` `sub0-neg_binary64_1770` `pow-sqr_binary64_1756` `associate-+l+_binary64_1716`
5×	`distribute-lft-out_binary64_1734`
4×	`mul-1-neg_binary64_1775` `remove-double-neg_binary64_1771`
3×	`cube-mult_binary64_1813` `rem-sqrt-square_binary64_1796` `associate--r+_binary64_1719`
2×	`unpow2_binary64_1848` `unpow1_binary64_1841` `*-lft-identity_binary64_1772` `+-lft-identity_binary64_1767` `div0_binary64_1764` `distribute-neg-out_binary64_1745`
1×	`unpow1/2_binary64_1847` `1-exp_binary64_1827` `rem-square-sqrt_binary64_1795` `associate--l+_binary64_1720` `associate-+r+_binary64_1715`
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` `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` `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-div_binary64_1812` `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` `/-rgt-identity_binary64_1774` `-rgt-identity_binary64_1773` `--rgt-identity_binary64_1769` `-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` `swap-sqr_binary64_1750` `cancel-sign-sub_binary64_1748` `distribute-frac-neg_binary64_1746` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `count-2_binary64_1731` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

23 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	319
1	133	296
2	350	296
3	1082	296
4	4297	296
5	5783	296

prune15.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	13	2	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	3	16

Error

14.6b

Counts

16 → 3

Compiler

Compiled 241 to 80 computations (66.8% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

14.6b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 14.6b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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 1-exp_binary64_1827 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 neg-mul-1_binary64_1779 neg-sub0_binary64_1778 unsub-neg_binary64_1777 sub-neg_binary64_1776 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 mul0-rgt_binary64_1766 mul0-lft_binary64_1765 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 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 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 distribute-rgt-in_binary64_1733 distribute-lft-in_binary64_1732 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_1724 associate-*r*_binary64_1723 associate--r-_binary64_1722 associate--l-_binary64_1721 associate--l+_binary64_1720 associate--r+_binary64_1719 associate-+l-_binary64_1718 associate-+r-_binary64_1717 associate-+l+_binary64_1716 associate-+r+_binary64_1715 *-commutative_binary64_1714 +-commutative_binary64_1713

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

14.6b

Counts

3 → 3

Compiler

Compiled 29 to 9 computations (69% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re)))))
29.6b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
29.6b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
29.6b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite204.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

14.6b

Rules

44×	`add-sqr-sqrt_binary64_1805`
40×	`cbrt-prod_binary64_1814`
29×	`sqrt-prod_binary64_1799`
19×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
18×	`sqrt-div_binary64_1800`
14×	`pow1_binary64_1844`
12×	`cbrt-div_binary64_1815`
11×	`swap-sqr_binary64_1750`
9×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `unswap-sqr_binary64_1751` `associate-l_binary64_1724` `associate-r_binary64_1723`
6×	`add-exp-log_binary64_1821` `pow1/3_binary64_1865`
4×	`add-log-exp_binary64_1822` `add-cbrt-cube_binary64_1819` `frac-times_binary64_1793`
3×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`
2×	`pow-prod-down_binary64_1854` `pow-prod-up_binary64_1853` `pow-sqr_binary64_1756` `associate-l/_binary64_1726` `associate-r/_binary64_1725`
1×	`pow2_binary64_1864` `pow-plus_binary64_1846` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `*-commutative_binary64_1714`

Counts

4 → 109

Calls

4 calls:

19.0ms	(.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

Compiler

Compiled 4667 to 431 computations (90.8% saved)

series348.0ms (9.9%)

Error

14.6b

Counts

4 → 30

Calls

4 calls:

109.0ms	(.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re)))))
70.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
69.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
67.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

Compiler

Compiled 2199 to 1027 computations (53.3% saved)

simplify117.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

615×	`associate-/l*_binary64_1728`
366×	`unswap-sqr_binary64_1751`
308×	`associate-l_binary64_1724`
299×	`cancel-sign-sub-inv_binary64_1749`
258×	`distribute-rgt-in_binary64_1733`
251×	`associate-r_binary64_1723`
230×	`distribute-lft-in_binary64_1732`
116×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729`
106×	`distribute-rgt-neg-in_binary64_1741`
98×	`distribute-lft-neg-in_binary64_1740`
92×	`times-frac_binary64_1789`
89×	`*-commutative_binary64_1714`
75×	`sqr-pow_binary64_1755`
63×	`distribute-rgt-out_binary64_1736`
61×	`sub-neg_binary64_1776`
53×	`log-prod_binary64_1869`
51×	`exp-prod_binary64_1835`
44×	`difference-of-squares_binary64_1752`
42×	`associate-/r*_binary64_1727`
41×	`cube-prod_binary64_1811`
32×	`swap-sqr_binary64_1750` `distribute-lft-out_binary64_1734`
29×	`distribute-lft-neg-out_binary64_1742`
25×	`associate-*l/_binary64_1726`
24×	`neg-sub0_binary64_1778` `*-lft-identity_binary64_1772` `distribute-rgt-out--_binary64_1737`
22×	`*-rgt-identity_binary64_1773`
21×	`pow-plus_binary64_1846` `neg-mul-1_binary64_1779`
19×	`+-commutative_binary64_1713`
17×	`distribute-rgt-neg-out_binary64_1743`
16×	`cube-unmult_binary64_1820` `associate-*r/_binary64_1725`
15×	`pow-sqr_binary64_1756`
11×	`rem-sqrt-square_binary64_1796` `distribute-lft-out--_binary64_1735` `associate-+l-_binary64_1718` `associate-+r-_binary64_1717`
10×	`+-rgt-identity_binary64_1768`
9×	`unpow3_binary64_1849` `distribute-neg-frac_binary64_1747` `associate-+l+_binary64_1716`
7×	`unsub-neg_binary64_1777`
6×	`log-pow_binary64_1872` `sub0-neg_binary64_1770` `distribute-neg-in_binary64_1744`
4×	`cube-mult_binary64_1813` `div-sub_binary64_1788` `count-2_binary64_1731` `associate-+r+_binary64_1715`
3×	`unpow1/2_binary64_1847` `associate--r+_binary64_1719`
2×	`unpow1/3_binary64_1850` `unpow2_binary64_1848` `unpow1_binary64_1841` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-square-sqrt_binary64_1795` `mul-1-neg_binary64_1775` `distribute-neg-out_binary64_1745`
1×	`1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-cbrt-cube_binary64_1807` `cancel-sign-sub_binary64_1748` `distribute-frac-neg_binary64_1746` `associate--l+_binary64_1720`
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` `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-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `/-rgt-identity_binary64_1774` `remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `+-lft-identity_binary64_1767` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `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-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

139 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	114	3594
1	228	3340
2	595	2972
3	1924	2954
4	5102	2954

prune112.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	86	3	89

Error

14.6b

Counts

89 → 3

Compiler

Compiled 2845 to 515 computations (81.9% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))))
5.2b	(exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 im im) (.f64 re re)))))
29.6b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
30.7b	(cbrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite96.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

14.6b

Rules

12×	`cbrt-prod_binary64_1814` `add-sqr-sqrt_binary64_1805`
11×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`pow1_binary64_1844` `cbrt-div_binary64_1815` `sqrt-prod_binary64_1799` `log-prod_binary64_1869` `exp-sum_binary64_1829`
5×	`exp-prod_binary64_1835`
4×	`add-log-exp_binary64_1822` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `flip3-+_binary64_1786` `flip-+_binary64_1757` `sqrt-div_binary64_1800`
3×	`pow1/3_binary64_1865`
2×	`log-pow_binary64_1872` `log-div_binary64_1870` `exp-diff_binary64_1831`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `rem-exp-log_binary64_1823`

Counts

4 → 65

Calls

4 calls:

6.0ms	(exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 im im) (.f64 re re)))))
5.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))))
4.0ms	(cbrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

Compiler

Compiled 2008 to 297 computations (85.2% saved)

series495.0ms (14%)

Error

14.6b

Counts

4 → 28

Calls

4 calls:

195.0ms	(exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 im im) (.f64 re re)))))
104.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))))
104.0ms	(cbrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
63.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

Compiler

Compiled 1745 to 1213 computations (30.5% saved)

simplify122.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

419×	`unswap-sqr_binary64_1751`
299×	`cancel-sign-sub-inv_binary64_1749`
250×	`distribute-rgt-in_binary64_1733`
244×	`associate-l_binary64_1724`
234×	`associate-r_binary64_1723`
222×	`distribute-lft-in_binary64_1732`
172×	`times-frac_binary64_1789`
154×	`log-pow_binary64_1872`
137×	`associate-/l*_binary64_1728`
131×	`log-prod_binary64_1869`
110×	`distribute-rgt-neg-in_binary64_1741`
100×	`distribute-lft-neg-in_binary64_1740`
99×	`sqr-pow_binary64_1755`
92×	`associate-/r*_binary64_1727`
90×	`*-commutative_binary64_1714`
81×	`exp-prod_binary64_1835`
67×	`sub-neg_binary64_1776`
53×	`prod-exp_binary64_1832`
48×	`distribute-rgt-out_binary64_1736`
44×	`difference-of-squares_binary64_1752` `associate-*l/_binary64_1726`
31×	`associate-*r/_binary64_1725`
30×	`neg-sub0_binary64_1778` `distribute-lft-neg-out_binary64_1742`
28×	`rem-exp-log_binary64_1823`
27×	`neg-mul-1_binary64_1779` `associate-/r/_binary64_1729`
25×	`pow-plus_binary64_1846` `distribute-lft-out_binary64_1734`
24×	`distribute-rgt-out--_binary64_1737`
23×	`unpow3_binary64_1849` `cube-unmult_binary64_1820`
22×	`distribute-rgt-neg-out_binary64_1743`
21×	`+-commutative_binary64_1713`
20×	`log-div_binary64_1870` `exp-sum_binary64_1829`
17×	`exp-to-pow_binary64_1845`
16×	`pow-sqr_binary64_1756`
11×	`distribute-lft-out--_binary64_1735` `associate-+l-_binary64_1718` `associate-+r-_binary64_1717`
10×	`log-rec_binary64_1871` `div-sub_binary64_1788` `+-rgt-identity_binary64_1768`
9×	`distribute-neg-frac_binary64_1747` `count-2_binary64_1731`
8×	`unpow1/3_binary64_1850` `div-exp_binary64_1834` `cube-prod_binary64_1811` `distribute-neg-in_binary64_1744`
7×	`unsub-neg_binary64_1777`
6×	`rem-sqrt-square_binary64_1796` `sub0-neg_binary64_1770` `associate-/l/_binary64_1730` `associate-+l+_binary64_1716`
4×	`exp-diff_binary64_1831` `exp-neg_binary64_1830` `swap-sqr_binary64_1750`
3×	`unpow2_binary64_1848` `rem-log-exp_binary64_1824` `cube-mult_binary64_1813` `distribute-frac-neg_binary64_1746` `associate--r+_binary64_1719`
2×	`unpow1/2_binary64_1847` `unpow1_binary64_1841` `exp-lft-sqr_binary64_1838` `rem-3cbrt-lft_binary64_1808` `mul-1-neg_binary64_1775` `distribute-neg-out_binary64_1745`
1×	`1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-cbrt-cube_binary64_1807` `rem-square-sqrt_binary64_1795` `cancel-sign-sub_binary64_1748` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate--l+_binary64_1720` `associate-+r+_binary64_1715`
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` `pow-base-0_binary64_1867` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `rec-exp_binary64_1833` `e-exp-1_binary64_1828` `exp-0_binary64_1825` `cube-div_binary64_1812` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `/-rgt-identity_binary64_1774` `-rgt-identity_binary64_1773` `-lft-identity_binary64_1772` `remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `+-lft-identity_binary64_1767` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `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` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

93 → 75

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	1491
1	289	1403
2	697	1403
3	2399	1383
4	4721	1359
5	4964	1359
6	4931	1359

prune79.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	75	3	78

Error

14.6b

Counts

78 → 3

Compiler

Compiled 1808 to 367 computations (79.7% saved)

regimes445.0ms (12.6%)

Accuracy

Total 7.0b remaining (95.2%)

Threshold costs 0b (0%)

Compiler

Compiled 2993 to 1469 computations (50.9% saved)

bsearch38.0ms (1.1%)

Steps

Iters	Range		Point
8	-2.2484782015030196e-162	-7.964990110451683e-165	-8.034323118303542e-165
8	-1.8155658953247407e+107	-5.5487109394741686e+104	-1.7917667196950207e+107

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64_1713`
1×	`neg-sub0_binary64_1778` `sub-neg_binary64_1776` `mul-1-neg_binary64_1775` `*-commutative_binary64_1714`
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` `neg-mul-1_binary64_1779` `unsub-neg_binary64_1777` `/-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	16	28
1	19	28
2	21	28
3	22	28
4	23	28
5	23	28

Compiler

Compiled 38 to 26 computations (31.6% saved)

end0.0ms (0%)

sample961.0ms (27.2%)

Algorithm

1×

intervals

Results

240.0ms

8000×

body

128

valid

Compiler

Compiled 385 to 196 computations (49.1% saved)

Details

analyze258.0ms (7.3%)

sample26.0ms (0.7%)

simplify8.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.2%)

rewrite19.0ms (0.5%)

series75.0ms (2.1%)

simplify56.0ms (1.6%)

prune15.0ms (0.4%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.2%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

rewrite204.0ms (5.8%)

series348.0ms (9.9%)

simplify117.0ms (3.3%)

prune112.0ms (3.2%)

localize13.0ms (0.4%)

rewrite96.0ms (2.7%)

series495.0ms (14%)

simplify122.0ms (3.5%)

prune79.0ms (2.2%)

regimes445.0ms (12.6%)

bsearch38.0ms (1.1%)

simplify11.0ms (0.3%)

end0.0ms (0%)

sample961.0ms (27.2%)

Profiling