Details

analyze175.0ms (2.3%)

Algorithm

1×	search
2×	egg-herbie

Rules

40×	`sub-neg_binary64_1776`
38×	`cancel-sign-sub-inv_binary64_1749`
26×	`distribute-rgt-in_binary64_1733` `associate--r+_binary64_1719`
24×	`distribute-rgt-neg-in_binary64_1741`
20×	`neg-mul-1_binary64_1779`
18×	`*-commutative_binary64_1714`
16×	`distribute-lft-neg-in_binary64_1740`
12×	`associate--r-_binary64_1722`
10×	`neg-sub0_binary64_1778` `sub0-neg_binary64_1770` `associate--l-_binary64_1721` `+-commutative_binary64_1713`
8×	`unsub-neg_binary64_1777` `distribute-neg-frac_binary64_1747` `associate-/l_binary64_1728` `associate-/r_binary64_1727` `associate--l+_binary64_1720`
6×	`*-lft-identity_binary64_1772` `distribute-lft-neg-out_binary64_1742` `associate-+l-_binary64_1718` `associate-+r+_binary64_1715`
4×	`remove-double-neg_binary64_1771` `+-rgt-identity_binary64_1768` `+-lft-identity_binary64_1767` `distribute-neg-in_binary64_1744` `distribute-rgt-neg-out_binary64_1743` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `associate-l/_binary64_1726` `associate-r/_binary64_1725` `associate-+r-_binary64_1717` `associate-+l+_binary64_1716`
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` `-rgt-identity_binary64_1773` `--rgt-identity_binary64_1769` `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_binary64_1748` `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` `distribute-lft-in_binary64_1732` `count-2_binary64_1731` `associate-l_binary64_1724` `associate-r_binary64_1723`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	18	24
2	26	24
3	36	24
4	50	24
5	89	24
6	105	24
7	151	24
8	153	24
9	179	24
10	208	24
11	241	24
12	271	24
13	284	24
14	246	24
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
74.9%	25%	0.1%	5
87.4%	12.5%	0.1%	6
87.4%	12.5%	0.1%	7
93.7%	6.2%	0.1%	8
93.7%	6.2%	0.1%	9
96.8%	3.1%	0.1%	10
96.8%	3.1%	0.1%	11
98.3%	1.6%	0.1%	12
98.3%	1.6%	0.1%	13
99.1%	0.8%	0.1%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample16.0ms (0.2%)

Algorithm

1×

intervals

Results

6.0ms	246×	body	128	valid
1.0ms	5×	body	2048	valid
0.0ms	3×	body	512	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 17 to 17 computations (0% saved)

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

24×	`sub-neg_binary64_1776` `cancel-sign-sub-inv_binary64_1749`
21×	`distribute-rgt-in_binary64_1733`
14×	`neg-mul-1_binary64_1779`
13×	`distribute-rgt-neg-in_binary64_1741`
12×	`unsub-neg_binary64_1777`
11×	`associate--r+_binary64_1719` `*-commutative_binary64_1714`
9×	`neg-sub0_binary64_1778`
8×	`distribute-lft-neg-in_binary64_1740` `associate-+l-_binary64_1718` `+-commutative_binary64_1713`
7×	`associate--r-_binary64_1722`
6×	`distribute-neg-in_binary64_1744`
5×	`*-lft-identity_binary64_1772` `sub0-neg_binary64_1770` `distribute-lft-neg-out_binary64_1742` `distribute-lft-in_binary64_1732` `associate--l-_binary64_1721` `associate--l+_binary64_1720` `associate-+l+_binary64_1716`
4×	`+-lft-identity_binary64_1767` `distribute-neg-frac_binary64_1747` `associate-/l_binary64_1728` `associate-/r_binary64_1727`
3×	`remove-double-neg_binary64_1771` `distribute-neg-out_binary64_1745` `distribute-rgt-neg-out_binary64_1743` `associate-+r+_binary64_1715`
2×	`-rgt-identity_binary64_1773` `--rgt-identity_binary64_1769` `distribute-lft-out--_binary64_1735` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `associate-l/_binary64_1726` `associate-*r/_binary64_1725` `associate-+r-_binary64_1717`
1×	`1-exp_binary64_1827` `+-rgt-identity_binary64_1768` `distribute-lft-out_binary64_1734`
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` `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_binary64_1748` `distribute-frac-neg_binary64_1746` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `distribute-rgt-out--_binary64_1737` `distribute-rgt-out_binary64_1736` `count-2_binary64_1731` `associate-l_binary64_1724` `associate-r*_binary64_1723`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	11	12
2	16	12
3	22	12
4	28	12
5	43	12
6	66	12
7	85	12
8	110	12
9	117	12
10	131	12
11	145	12
12	165	12
13	187	12
14	197	12
15	159	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

0.1b

Counts

1 → 1

Compiler

Compiled 8 to 7 computations (12.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

3×	`add-log-exp_binary64_1822` `*-un-lft-identity_binary64_1783`
1×	`sum-log_binary64_1874` `pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805` `flip3-+_binary64_1786` `flip-+_binary64_1757` `distribute-lft-out_binary64_1734` `+-commutative_binary64_1713`

Counts

1 → 12

Calls

1 calls:

6.0ms

(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

Compiler

Compiled 209 to 102 computations (51.2% saved)

series107.0ms (1.4%)

Error

0.1b

Counts

1 → 9

Calls

1 calls:

102.0ms

(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

Compiler

Compiled 160 to 118 computations (26.3% saved)

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Rules

849×	`div-sub_binary64_1788`
474×	`times-frac_binary64_1789`
416×	`distribute-rgt-out_binary64_1736`
331×	`distribute-rgt-in_binary64_1733`
315×	`associate-+l+_binary64_1716`
313×	`cancel-sign-sub-inv_binary64_1749`
265×	`distribute-lft-in_binary64_1732`
253×	`associate-+r+_binary64_1715`
212×	`unsub-neg_binary64_1777`
161×	`distribute-rgt-neg-out_binary64_1743`
160×	`distribute-lft-neg-out_binary64_1742`
155×	`associate-l_binary64_1724`
146×	`unswap-sqr_binary64_1751`
144×	`associate-/l*_binary64_1728`
139×	`sub-neg_binary64_1776`
113×	`associate-r_binary64_1723`
98×	`associate-*l/_binary64_1726`
85×	`distribute-rgt-neg-in_binary64_1741`
80×	`distribute-frac-neg_binary64_1746`
79×	`*-commutative_binary64_1714`
71×	`distribute-lft-neg-in_binary64_1740`
70×	`associate-*r/_binary64_1725`
62×	`associate-/l/_binary64_1730`
59×	`neg-mul-1_binary64_1779`
56×	`distribute-neg-frac_binary64_1747`
55×	`+-commutative_binary64_1713`
53×	`distribute-neg-in_binary64_1744`
52×	`neg-sub0_binary64_1778` `associate-+l-_binary64_1718`
50×	`distribute-rgt-out--_binary64_1737` `associate--r+_binary64_1719`
49×	`associate-/r/_binary64_1729`
37×	`cancel-sign-sub_binary64_1748`
31×	`distribute-neg-out_binary64_1745`
30×	`mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `sqr-pow_binary64_1755`
29×	`associate-/r*_binary64_1727`
23×	`cube-prod_binary64_1811` `sub0-neg_binary64_1770`
21×	`associate-+r-_binary64_1717`
16×	`distribute-lft-out_binary64_1734`
15×	`cube-unmult_binary64_1820`
13×	`exp-prod_binary64_1835`
12×	`unpow3_binary64_1849` `pow-plus_binary64_1846` `remove-double-neg_binary64_1771`
10×	`exp-sum_binary64_1829` `+-rgt-identity_binary64_1768` `associate--l+_binary64_1720`
9×	`associate--r-_binary64_1722`
8×	`exp-diff_binary64_1831` `div0_binary64_1764`
5×	`cube-mult_binary64_1813` `distribute-rgt1-in_binary64_1739`
4×	`cube-div_binary64_1812` `cube-neg_binary64_1810` `sqr-neg_binary64_1797` `swap-sqr_binary64_1750`
3×	`*-lft-identity_binary64_1772` `+-lft-identity_binary64_1767` `difference-of-squares_binary64_1752` `associate--l-_binary64_1721`
2×	`unpow2_binary64_1848` `exp-sqrt_binary64_1836` `exp-neg_binary64_1830` `pow-sqr_binary64_1756` `distribute-lft-out--_binary64_1735` `count-2_binary64_1731`
1×	`prod-exp_binary64_1832` `1-exp_binary64_1827` `sqr-abs_binary64_1798`
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` `unpow1/2_binary64_1847` `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` `div-exp_binary64_1834` `rec-exp_binary64_1833` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `rem-sqrt-square_binary64_1796` `rem-square-sqrt_binary64_1795` `mul-1-neg_binary64_1775` `/-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` `distribute-lft1-in_binary64_1738`

Counts

21 → 9

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	334
1	91	309
2	187	302
3	404	302
4	962	302
5	2561	302
6	3998	302
7	5086	302

prune12.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	7	2	9
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	7	3	10

Error

0.0b

Counts

10 → 3

Compiler

Compiled 194 to 103 computations (46.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))
0.0b	(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
0.0b	(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
0.4b	(.f64 (sqrt.f64 (+.f64 x (.f64 1/2 (fabs.f64 (-.f64 y x))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))

rewrite194.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`add-sqr-sqrt_binary64_1805`
24×	`sqrt-prod_binary64_1799`
21×	`pow1_binary64_1844`
16×	`sqrt-div_binary64_1800`
14×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
9×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
8×	`swap-sqr_binary64_1750`
6×	`add-exp-log_binary64_1821` `add-log-exp_binary64_1822` `add-cbrt-cube_binary64_1819` `associate-l_binary64_1724` `associate-r_binary64_1723`
5×	`pow-prod-up_binary64_1853`
4×	`rem-sqrt-square_binary64_1796` `frac-times_binary64_1793` `unswap-sqr_binary64_1751`
3×	`pow-prod-down_binary64_1854` `pow-sqr_binary64_1756`
2×	`associate-l/_binary64_1726` `associate-r/_binary64_1725`
1×	`pow2_binary64_1864` `pow-plus_binary64_1846` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `sqrt-unprod_binary64_1803` `sqr-abs_binary64_1798` `rem-square-sqrt_binary64_1795` `*-commutative_binary64_1714` `sum-log_binary64_1874` `+-commutative_binary64_1713`

Counts

4 → 99

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (+.f64 x (.f64 1/2 (fabs.f64 (-.f64 y x))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
3.0ms	(+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))
3.0ms	(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
3.0ms	(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))

Compiler

Compiled 3144 to 1616 computations (48.6% saved)

series508.0ms (6.7%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

141.0ms	(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
133.0ms	(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
102.0ms	(.f64 (sqrt.f64 (+.f64 x (.f64 1/2 (fabs.f64 (-.f64 y x))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
96.0ms	(+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))

Compiler

Compiled 1846 to 1207 computations (34.6% saved)

simplify168.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

682×	`times-frac_binary64_1789`
444×	`associate-l_binary64_1724`
365×	`associate-r_binary64_1723`
260×	`cancel-sign-sub-inv_binary64_1749`
195×	`unswap-sqr_binary64_1751`
151×	`distribute-rgt-out_binary64_1736`
135×	`*-commutative_binary64_1714`
127×	`distribute-rgt-neg-in_binary64_1741`
119×	`distribute-lft-neg-in_binary64_1740`
107×	`distribute-lft-out_binary64_1734`
100×	`distribute-rgt-in_binary64_1733`
91×	`distribute-lft-in_binary64_1732`
90×	`distribute-neg-frac_binary64_1747`
85×	`exp-prod_binary64_1835`
76×	`log-prod_binary64_1869`
74×	`associate-/l*_binary64_1728`
68×	`associate-*r/_binary64_1725`
66×	`sqr-pow_binary64_1755`
65×	`cube-prod_binary64_1811`
61×	`associate-*l/_binary64_1726`
53×	`sub-neg_binary64_1776` `associate-/r*_binary64_1727`
52×	`div-sub_binary64_1788`
47×	`swap-sqr_binary64_1750`
34×	`unpow3_binary64_1849`
33×	`neg-sub0_binary64_1778`
31×	`neg-mul-1_binary64_1779`
30×	`rem-sqrt-square_binary64_1796`
28×	`+-commutative_binary64_1713`
27×	`pow-plus_binary64_1846` `associate-+l+_binary64_1716`
22×	`cube-unmult_binary64_1820` `associate-+r+_binary64_1715`
19×	`-rgt-identity_binary64_1773` `-lft-identity_binary64_1772`
15×	`cube-mult_binary64_1813` `distribute-lft-neg-out_binary64_1742`
14×	`log-pow_binary64_1872`
13×	`pow-sqr_binary64_1756` `distribute-rgt-out--_binary64_1737` `associate-+r-_binary64_1717`
12×	`+-rgt-identity_binary64_1768` `associate--l+_binary64_1720`
11×	`distribute-rgt-neg-out_binary64_1743`
10×	`unsub-neg_binary64_1777` `associate-+l-_binary64_1718`
9×	`rem-square-sqrt_binary64_1795`
8×	`distribute-neg-in_binary64_1744`
6×	`exp-sum_binary64_1829` `sub0-neg_binary64_1770`
5×	`distribute-lft-out--_binary64_1735`
4×	`unpow2_binary64_1848` `unpow1/2_binary64_1847` `associate-/r/_binary64_1729`
2×	`difference-of-squares_binary64_1752` `count-2_binary64_1731`
1×	`unpow1_binary64_1841` `prod-exp_binary64_1832` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-cbrt-cube_binary64_1807` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797`
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` `div-exp_binary64_1834` `rec-exp_binary64_1833` `exp-diff_binary64_1831` `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` `cube-neg_binary64_1810` `rem-cube-cbrt_binary64_1806` `mul-1-neg_binary64_1775` `/-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` `cancel-sign-sub_binary64_1748` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate-/l/_binary64_1730` `associate--r-_binary64_1722` `associate--l-_binary64_1721` `associate--r+_binary64_1719`

Counts

135 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	2903
1	248	2722
2	706	2670
3	2410	2577
4	4833	2577
5	4915	2577
6	5004	2577

prune109.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	75	5	80

Error

0.0b

Counts

80 → 5

Compiler

Compiled 2020 to 1064 computations (47.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (+.f64 x (.f64 1/2 (fabs.f64 (-.f64 y x))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
0.5b	(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
0.5b	(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
0.5b	(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))

rewrite267.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`cbrt-prod_binary64_1814`
23×	`add-sqr-sqrt_binary64_1805`
18×	`cbrt-div_binary64_1815`
15×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
11×	`pow1_binary64_1844`
9×	`pow1/3_binary64_1865` `flip3-+_binary64_1786` `flip-+_binary64_1757`
6×	`add-exp-log_binary64_1821` `swap-sqr_binary64_1750` `associate-l_binary64_1724` `associate-r_binary64_1723`
4×	`add-log-exp_binary64_1822` `add-cbrt-cube_binary64_1819` `frac-times_binary64_1793` `unswap-sqr_binary64_1751`
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 → 87

Calls

4 calls:

10.0ms	(.f64 (cbrt.f64 (+.f64 x (.f64 1/2 (fabs.f64 (-.f64 y x))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
3.0ms	(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
3.0ms	(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
3.0ms	(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))

Compiler

Compiled 4802 to 2524 computations (47.4% saved)

series1.8s (23.6%)

Error

0.0b

Counts

4 → 51

Calls

4 calls:

509.0ms	(.f64 (cbrt.f64 (+.f64 x (.f64 1/2 (fabs.f64 (-.f64 y x))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
396.0ms	(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
376.0ms	(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
375.0ms	(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))

Compiler

Compiled 6058 to 3821 computations (36.9% saved)

simplify205.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

409×	`*-commutative_binary64_1714`
337×	`distribute-rgt-in_binary64_1733`
318×	`distribute-lft-in_binary64_1732`
304×	`cancel-sign-sub-inv_binary64_1749`
268×	`unswap-sqr_binary64_1751`
211×	`distribute-rgt-neg-in_binary64_1741`
205×	`distribute-lft-neg-in_binary64_1740`
170×	`associate-r_binary64_1723`
168×	`sqr-pow_binary64_1755`
144×	`log-prod_binary64_1869`
132×	`associate-l_binary64_1724`
129×	`sub-neg_binary64_1776`
75×	`associate-+l+_binary64_1716`
68×	`+-commutative_binary64_1713`
64×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
63×	`log-pow_binary64_1872` `distribute-rgt-out_binary64_1736`
59×	`associate-+r+_binary64_1715`
58×	`exp-prod_binary64_1835`
45×	`associate-/r*_binary64_1727`
36×	`cube-prod_binary64_1811`
32×	`distribute-rgt-out--_binary64_1737` `associate--l+_binary64_1720`
30×	`unsub-neg_binary64_1777`
28×	`associate-+r-_binary64_1717`
27×	`+-rgt-identity_binary64_1768` `swap-sqr_binary64_1750`
24×	`distribute-lft-out_binary64_1734`
23×	`associate-+l-_binary64_1718`
22×	`pow-sqr_binary64_1756`
21×	`unpow1/3_binary64_1850` `unpow3_binary64_1849`
17×	`pow-plus_binary64_1846` `exp-sum_binary64_1829`
16×	`rem-sqrt-square_binary64_1796`
14×	`-rgt-identity_binary64_1773` `-lft-identity_binary64_1772` `sub0-neg_binary64_1770`
12×	`cube-unmult_binary64_1820` `distribute-lft-neg-out_binary64_1742`
10×	`distribute-neg-in_binary64_1744`
9×	`distribute-lft-out--_binary64_1735`
7×	`exp-diff_binary64_1831`
6×	`div-sub_binary64_1788` `distribute-rgt-neg-out_binary64_1743`
5×	`log-div_binary64_1870` `cube-mult_binary64_1813` `associate-/l*_binary64_1728`
4×	`unpow1/2_binary64_1847`
3×	`unpow2_binary64_1848` `unpow1_binary64_1841` `rem-exp-log_binary64_1823` `count-2_binary64_1731` `associate--r-_binary64_1722`
2×	`log-rec_binary64_1871` `exp-to-pow_binary64_1845` `exp-neg_binary64_1830` `rem-3cbrt-lft_binary64_1808` `+-lft-identity_binary64_1767` `difference-of-squares_binary64_1752` `associate-/l/_binary64_1730` `associate--r+_binary64_1719`
1×	`log-E_binary64_1873` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-3cbrt-rft_binary64_1809` `rem-cbrt-cube_binary64_1807` `sqr-abs_binary64_1798` `rem-square-sqrt_binary64_1795` `remove-double-neg_binary64_1771` `+-inverses_binary64_1762` `distribute-rgt1-in_binary64_1739`
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` `pow-base-0_binary64_1867` `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` `e-exp-1_binary64_1828` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `cube-div_binary64_1812` `cube-neg_binary64_1810` `rem-cube-cbrt_binary64_1806` `sqr-neg_binary64_1797` `times-frac_binary64_1789` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `--rgt-identity_binary64_1769` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `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` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-lft1-in_binary64_1738` `associate-/r/_binary64_1729` `associate-l/_binary64_1726` `associate-*r/_binary64_1725` `associate--l-_binary64_1721`

Counts

138 → 101

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	4399
1	451	4105
2	1292	3983
3	2673	3965
4	4870	3965
5	4992	3965
6	4906	3965

prune253.0ms (3.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	100	6	106

Error

0.0b

Counts

106 → 6

Compiler

Compiled 5074 to 2729 computations (46.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
0.2b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (.f64 1/2 (fabs.f64 (-.f64 y x)))))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 3))
0.6b	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 3)

rewrite406.0ms (5.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

107×	`sqrt-prod_binary64_1799`
74×	`add-sqr-sqrt_binary64_1805`
36×	`sqrt-div_binary64_1800`
27×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
25×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
24×	`unswap-sqr_binary64_1751` `associate-r_binary64_1723`
12×	`pow1_binary64_1844` `sqrt-pow1_binary64_1801`
10×	`add-exp-log_binary64_1821`
9×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-l_binary64_1724`
8×	`cube-div_binary64_1812`
7×	`add-cbrt-cube_binary64_1819`
6×	`pow1/2_binary64_1863`
5×	`pow-pow_binary64_1855` `sqr-pow_binary64_1755`
4×	`add-log-exp_binary64_1822` `frac-times_binary64_1793` `rem-sqrt-square_binary64_1796`
3×	`pow-unpow_binary64_1860` `prod-exp_binary64_1832`
2×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `unpow3_binary64_1849` `cube-mult_binary64_1813` `associate-l/_binary64_1726` `associate-r/_binary64_1725`
1×	`rem-cube-cbrt_binary64_1806` `sqrt-pow2_binary64_1802` `pow-prod-up_binary64_1853` `cbrt-unprod_binary64_1816` `*-commutative_binary64_1714`

Counts

4 → 162

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (.f64 1/2 (fabs.f64 (-.f64 y x)))))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 3))
8.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 3)
4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))

Compiler

Compiled 6363 to 3765 computations (40.8% saved)

series1.6s (20.5%)

Error

0.0b

Counts

4 → 45

Calls

4 calls:

604.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 3)
386.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
381.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
107.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (.f64 1/2 (fabs.f64 (-.f64 y x)))))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 3))

Compiler

Compiled 3126 to 2214 computations (29.2% saved)

simplify233.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

357×	`sqr-pow_binary64_1755`
284×	`associate-r_binary64_1723`
269×	`log-prod_binary64_1869`
267×	`associate-l_binary64_1724`
255×	`exp-prod_binary64_1835`
251×	`cancel-sign-sub-inv_binary64_1749`
166×	`distribute-rgt-neg-in_binary64_1741`
162×	`cube-prod_binary64_1811`
135×	`sub-neg_binary64_1776`
132×	`swap-sqr_binary64_1750`
101×	`*-commutative_binary64_1714`
99×	`distribute-lft-neg-in_binary64_1740`
94×	`unpow3_binary64_1849`
85×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
76×	`+-commutative_binary64_1713`
75×	`associate-+l+_binary64_1716`
65×	`pow-sqr_binary64_1756` `associate-+r+_binary64_1715`
60×	`log-pow_binary64_1872`
56×	`unswap-sqr_binary64_1751` `distribute-rgt-in_binary64_1733`
52×	`pow-plus_binary64_1846`
49×	`cube-mult_binary64_1813`
47×	`distribute-lft-in_binary64_1732`
45×	`associate-/r*_binary64_1727`
39×	`associate--l+_binary64_1720`
36×	`rem-sqrt-square_binary64_1796`
30×	`associate-+r-_binary64_1717`
29×	`unsub-neg_binary64_1777` `+-rgt-identity_binary64_1768`
26×	`associate-/l*_binary64_1728`
24×	`exp-sum_binary64_1829`
23×	`associate-+l-_binary64_1718`
19×	`*-rgt-identity_binary64_1773` `distribute-rgt-out_binary64_1736`
18×	`*-lft-identity_binary64_1772`
15×	`rem-square-sqrt_binary64_1795` `distribute-rgt-out--_binary64_1737`
14×	`sub0-neg_binary64_1770`
11×	`distribute-lft-neg-out_binary64_1742`
10×	`unpow2_binary64_1848` `distribute-neg-in_binary64_1744`
8×	`unpow1/2_binary64_1847` `unpow1_binary64_1841` `distribute-lft-out_binary64_1734`
7×	`exp-diff_binary64_1831` `cube-unmult_binary64_1820`
6×	`div-sub_binary64_1788` `distribute-rgt-neg-out_binary64_1743`
5×	`log-div_binary64_1870`
4×	`exp-to-pow_binary64_1845` `+-lft-identity_binary64_1767` `distribute-lft-out--_binary64_1735` `count-2_binary64_1731`
3×	`prod-exp_binary64_1832` `rem-exp-log_binary64_1823` `associate-/l/_binary64_1730` `associate-*r/_binary64_1725` `associate--r-_binary64_1722`
2×	`log-rec_binary64_1871` `exp-neg_binary64_1830` `rem-cbrt-cube_binary64_1807` `sqr-abs_binary64_1798` `difference-of-squares_binary64_1752` `associate--r+_binary64_1719`
1×	`1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-cube-cbrt_binary64_1806` `remove-double-neg_binary64_1771` `+-inverses_binary64_1762` `distribute-rgt1-in_binary64_1739` `associate-/r/_binary64_1729`
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` `unpow1/3_binary64_1850` `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` `e-exp-1_binary64_1828` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `cube-div_binary64_1812` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `sqr-neg_binary64_1797` `times-frac_binary64_1789` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `--rgt-identity_binary64_1769` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `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` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-lft1-in_binary64_1738` `associate-l/_binary64_1726` `associate--l-_binary64_1721`

Counts

207 → 147

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	236	6115
1	595	5663
2	1975	5369
3	3418	5311
4	4776	5309
5	4954	5309

prune244.0ms (3.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	2	0	2
Picked	1	0	1
Done	0	3	3
Total	147	6	153

Error

Counts

153 → 6

Compiler

Compiled 4360 to 2519 computations (42.2% saved)

regimes196.0ms (2.6%)

Accuracy

Total 0.0b remaining (85.6%)

Threshold costs 0.0b (85.6%)

Compiler

Compiled 2078 to 1402 computations (32.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64_1713`
2×	`sub-neg_binary64_1776`
1×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778` `*-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` `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	8	12
1	11	12
2	16	12
3	18	12
4	19	12
5	19	12

end0.0ms (0%)

sample995.0ms (13.1%)

Algorithm

1×

intervals

Results

185.0ms	7719×	body	128	valid
14.0ms	85×	body	2048	valid
8.0ms	95×	body	1024	valid
4.0ms	62×	body	512	valid
2.0ms	39×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 703 to 477 computations (32.1% saved)

Iter	Nodes	Cost
0	12	24
1	18	24
2	26	24
3	36	24
4	50	24
5	89	24
6	105	24
7	151	24
8	153	24
9	179	24
10	208	24
11	241	24
12	271	24
13	284	24
14	246	24
0	2	2
1	2	2

Iter	Nodes	Cost
0	8	12
1	11	12
2	16	12
3	22	12
4	28	12
5	43	12
6	66	12
7	85	12
8	110	12
9	117	12
10	131	12
11	145	12
12	165	12
13	187	12
14	197	12
15	159	12

Iter	Nodes	Cost
0	12	24
1	18	24
2	26	24
3	36	24
4	50	24
5	89	24
6	105	24
7	151	24
8	153	24
9	179	24
10	208	24
11	241	24
12	271	24
13	284	24
14	246	24
0	2	2
1	2	2

Iter	Nodes	Cost
0	8	12
1	11	12
2	16	12
3	22	12
4	28	12
5	43	12
6	66	12
7	85	12
8	110	12
9	117	12
10	131	12
11	145	12
12	165	12
13	187	12
14	197	12
15	159	12

Details

analyze175.0ms (2.3%)

sample16.0ms (0.2%)

simplify17.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite20.0ms (0.3%)

series107.0ms (1.4%)

simplify72.0ms (1%)

prune12.0ms (0.2%)

localize8.0ms (0.1%)

rewrite194.0ms (2.6%)

series508.0ms (6.7%)

simplify168.0ms (2.2%)

prune109.0ms (1.4%)

localize13.0ms (0.2%)

rewrite267.0ms (3.5%)

series1.8s (23.6%)

simplify205.0ms (2.7%)

prune253.0ms (3.3%)

localize10.0ms (0.1%)

rewrite406.0ms (5.4%)

series1.6s (20.5%)

simplify233.0ms (3.1%)

prune244.0ms (3.2%)

regimes196.0ms (2.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample995.0ms (13.1%)

Profiling

Iter	Nodes	Cost
0	12	24
1	18	24
2	26	24
3	36	24
4	50	24
5	89	24
6	105	24
7	151	24
8	153	24
9	179	24
10	208	24
11	241	24
12	271	24
13	284	24
14	246	24
0	2	2
1	2	2

Iter	Nodes	Cost
0	8	12
1	11	12
2	16	12
3	22	12
4	28	12
5	43	12
6	66	12
7	85	12
8	110	12
9	117	12
10	131	12
11	145	12
12	165	12
13	187	12
14	197	12
15	159	12