Details

analyze341.0ms (2.9%)

Algorithm

1×	search
2×	egg-herbie

Rules

478×	`sub-neg_binary64_1776`
434×	`distribute-rgt-in_binary64_1733` `associate-+l+_binary64_1716`
406×	`associate-l_binary64_1724`
374×	`associate-+r+_binary64_1715`
354×	`associate--l+_binary64_1720`
350×	`*-commutative_binary64_1714`
326×	`associate-r_binary64_1723`
291×	`distribute-lft-in_binary64_1732`
286×	`distribute-rgt-out_binary64_1736`
280×	`neg-mul-1_binary64_1779`
244×	`unsub-neg_binary64_1777`
194×	`neg-sub0_binary64_1778`
142×	`associate-+l-_binary64_1718`
130×	`+-commutative_binary64_1713`
119×	`distribute-rgt-neg-out_binary64_1743`
118×	`distribute-lft-neg-out_binary64_1742`
112×	`distribute-lft-out_binary64_1734`
93×	`cancel-sign-sub-inv_binary64_1749`
84×	`associate-+r-_binary64_1717`
58×	`associate--r+_binary64_1719`
40×	`distribute-rgt-neg-in_binary64_1741`
38×	`unswap-sqr_binary64_1751`
29×	`distribute-lft-neg-in_binary64_1740`
22×	`associate--r-_binary64_1722`
20×	`*-rgt-identity_binary64_1773`
19×	`*-lft-identity_binary64_1772`
18×	`distribute-neg-in_binary64_1744`
14×	`sqr-pow_binary64_1755`
8×	`difference-of-sqr--1_binary64_1754`
7×	`pow-plus_binary64_1846`
6×	`mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `swap-sqr_binary64_1750` `distribute-lft1-in_binary64_1738`
5×	`cube-unmult_binary64_1820`
4×	`difference-of-sqr-1_binary64_1753`
2×	`unpow2_binary64_1848` `mul-1-neg_binary64_1775` `sub0-neg_binary64_1770`
1×	`unpow3_binary64_1849` `unpow1/2_binary64_1847` `unpow1_binary64_1841` `1-exp_binary64_1827` `cube-prod_binary64_1811` `rem-sqrt-square_binary64_1796` `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` `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-mult_binary64_1813` `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` `rem-square-sqrt_binary64_1795` `times-frac_binary64_1789` `div-sub_binary64_1788` `/-rgt-identity_binary64_1774` `remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `+-rgt-identity_binary64_1768` `+-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` `pow-sqr_binary64_1756` `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-rgt-out--_binary64_1737` `distribute-lft-out--_binary64_1735` `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	31	92
1	100	92
2	254	92
3	765	92
4	2201	92
5	4207	92
6	4979	92
7	5012	92
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
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 22 computations (31.3% saved)

sample26.0ms (0.2%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

669×	`unsub-neg_binary64_1777`
596×	`cancel-sign-sub-inv_binary64_1749`
373×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
340×	`+-commutative_binary64_1713`
277×	`sub-neg_binary64_1776`
242×	`distribute-rgt-neg-in_binary64_1741`
232×	`associate-+l+_binary64_1716`
220×	`*-commutative_binary64_1714`
212×	`associate-l_binary64_1724`
192×	`associate-+r+_binary64_1715`
188×	`associate--l+_binary64_1720`
185×	`associate-r_binary64_1723`
174×	`distribute-rgt-in_binary64_1733`
149×	`distribute-rgt-out_binary64_1736`
147×	`distribute-lft-in_binary64_1732`
146×	`distribute-neg-in_binary64_1744`
134×	`distribute-lft-neg-out_binary64_1742`
113×	`distribute-rgt-neg-out_binary64_1743`
84×	`unswap-sqr_binary64_1751`
72×	`associate-+l-_binary64_1718`
66×	`cancel-sign-sub_binary64_1748`
45×	`associate-+r-_binary64_1717`
38×	`distribute-lft-out_binary64_1734` `associate--r+_binary64_1719`
27×	`*-rgt-identity_binary64_1773`
26×	`distribute-lft-neg-in_binary64_1740`
20×	`*-lft-identity_binary64_1772`
19×	`sqr-pow_binary64_1755`
11×	`associate--r-_binary64_1722`
10×	`sub0-neg_binary64_1770`
9×	`pow-plus_binary64_1846` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765`
8×	`+-rgt-identity_binary64_1768` `difference-of-sqr--1_binary64_1754`
6×	`cube-unmult_binary64_1820` `swap-sqr_binary64_1750`
5×	`rem-sqrt-square_binary64_1796` `difference-of-sqr-1_binary64_1753` `distribute-lft1-in_binary64_1738`
4×	`distribute-neg-out_binary64_1745`
3×	`unpow2_binary64_1848` `cube-prod_binary64_1811`
2×	`mul-1-neg_binary64_1775`
1×	`unpow3_binary64_1849` `unpow1/2_binary64_1847` `unpow1_binary64_1841` `1-exp_binary64_1827` `remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `pow-sqr_binary64_1756` `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` `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-mult_binary64_1813` `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` `rem-square-sqrt_binary64_1795` `times-frac_binary64_1789` `div-sub_binary64_1788` `/-rgt-identity_binary64_1774` `+-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-squares_binary64_1752` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-rgt-out--_binary64_1737` `distribute-lft-out--_binary64_1735` `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`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	46
1	61	46
2	152	46
3	438	46
4	1297	46
5	2508	46
6	4605	46
7	5029	46

prune4.0ms (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 62 to 42 computations (32.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.0b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.8b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite238.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`pow1_binary64_1844` `add-exp-log_binary64_1821`
14×	`add-cbrt-cube_binary64_1819`
10×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
8×	`add-cube-cbrt_binary64_1818`
7×	`associate-r_binary64_1723`
6×	`pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `add-log-exp_binary64_1822` `cbrt-unprod_binary64_1816`
4×	`distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `associate-*r/_binary64_1725`
3×	`unpow-prod-down_binary64_1862` `pow-unpow_binary64_1860`
2×	`unswap-sqr_binary64_1751` `sub-neg_binary64_1776` `cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-+r+_binary64_1715`
1×	`flip3--_binary64_1787` `flip--_binary64_1758` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `unpow2_binary64_1848` `sqr-pow_binary64_1755` `distribute-lft-out_binary64_1734` `sum-log_binary64_1874` `+-commutative_binary64_1713`

Counts

4 → 80

Calls

4 calls:

10.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
9.0ms	(.f64 (.f64 a a) (+.f64 1 a))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 3109 to 1674 computations (46.2% saved)

series1.2s (9.8%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

591.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
299.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
139.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
69.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 2909 to 2263 computations (22.2% saved)

simplify90.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

853×	`distribute-rgt-in_binary64_1733`
794×	`distribute-lft-in_binary64_1732`
274×	`cancel-sign-sub-inv_binary64_1749`
246×	`associate-l_binary64_1724`
204×	`associate-r_binary64_1723`
122×	`distribute-rgt-neg-in_binary64_1741`
109×	`*-commutative_binary64_1714`
104×	`distribute-lft-neg-in_binary64_1740`
95×	`unswap-sqr_binary64_1751`
85×	`distribute-rgt-out_binary64_1736`
71×	`+-commutative_binary64_1713`
69×	`sqr-pow_binary64_1755`
63×	`exp-prod_binary64_1835`
58×	`associate-+r+_binary64_1715`
55×	`distribute-lft-out_binary64_1734`
49×	`associate-+l+_binary64_1716`
43×	`sub-neg_binary64_1776`
42×	`log-prod_binary64_1869`
36×	`associate--l+_binary64_1720`
35×	`distribute-neg-in_binary64_1744`
31×	`distribute-lft-neg-out_binary64_1742`
29×	`neg-sub0_binary64_1778`
28×	`neg-mul-1_binary64_1779` `*-lft-identity_binary64_1772`
27×	`exp-sum_binary64_1829`
23×	`cube-prod_binary64_1811`
22×	`*-rgt-identity_binary64_1773`
20×	`distribute-rgt-out--_binary64_1737`
19×	`swap-sqr_binary64_1750` `distribute-rgt-neg-out_binary64_1743`
12×	`cube-unmult_binary64_1820` `pow-sqr_binary64_1756`
9×	`pow-plus_binary64_1846` `unsub-neg_binary64_1777`
8×	`distribute-lft-out--_binary64_1735`
7×	`log-pow_binary64_1872`
6×	`unpow3_binary64_1849` `unpow2_binary64_1848` `unpow1/2_binary64_1847` `unpow1_binary64_1841`
5×	`cube-mult_binary64_1813`
2×	`exp-diff_binary64_1831` `rem-sqrt-square_binary64_1796` `distribute-rgt1-in_binary64_1739` `count-2_binary64_1731` `associate--r+_binary64_1719`
1×	`prod-exp_binary64_1832` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-3cbrt-rft_binary64_1809` `rem-square-sqrt_binary64_1795` `div-sub_binary64_1788` `difference-of-squares_binary64_1752` `associate-/l*_binary64_1728` `associate-+l-_binary64_1718` `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-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-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-3cbrt-lft_binary64_1808` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `times-frac_binary64_1789` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `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` `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_1730` `associate-/r/_binary64_1729` `associate-/r_binary64_1727` `associate-l/_binary64_1726` `associate-r/_binary64_1725` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

133 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	3004
1	533	2688
2	1756	2603
3	5452	2603

prune154.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	4	106

Error

0.0b

Counts

106 → 4

Compiler

Compiled 2301 to 1269 computations (44.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
0.0b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))
0.7b	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a))))
0.8b	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

rewrite363.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`add-log-exp_binary64_1822`
14×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
8×	`add-sqr-sqrt_binary64_1805` `associate-*r/_binary64_1725`
7×	`sum-log_binary64_1874`
6×	`pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `add-cube-cbrt_binary64_1818` `cbrt-unprod_binary64_1816` `-un-lft-identity_binary64_1783` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `associate-r*_binary64_1723`
5×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
4×	`sub-neg_binary64_1776` `cancel-sign-sub-inv_binary64_1749` `frac-add_binary64_1791` `associate-+r+_binary64_1715`
3×	`flip3--_binary64_1787` `flip--_binary64_1758` `associate-+l+_binary64_1716`
2×	`unswap-sqr_binary64_1751` `associate-l_binary64_1724` `*-commutative_binary64_1714` `+-commutative_binary64_1713`

Counts

4 → 83

Calls

4 calls:

22.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
16.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))
12.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a))))
8.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 4436 to 2844 computations (35.9% saved)

series1.6s (13.6%)

Error

0.0b

Counts

4 → 56

Calls

4 calls:

607.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
513.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))
284.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a))))
148.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 3339 to 2731 computations (18.2% saved)

simplify197.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

501×	`cancel-sign-sub-inv_binary64_1749`
396×	`associate-l_binary64_1724`
356×	`associate-r_binary64_1723`
252×	`distribute-rgt-neg-in_binary64_1741`
226×	`distribute-rgt-in_binary64_1733`
221×	`*-commutative_binary64_1714`
213×	`distribute-lft-in_binary64_1732`
173×	`unswap-sqr_binary64_1751`
108×	`+-commutative_binary64_1713`
104×	`distribute-neg-in_binary64_1744`
99×	`sub-neg_binary64_1776`
86×	`associate-+l+_binary64_1716`
83×	`associate-+r+_binary64_1715`
80×	`exp-prod_binary64_1835`
76×	`sqr-pow_binary64_1755`
71×	`distribute-lft-neg-out_binary64_1742`
61×	`exp-sum_binary64_1829`
60×	`cube-prod_binary64_1811`
52×	`neg-sub0_binary64_1778`
51×	`neg-mul-1_binary64_1779`
47×	`distribute-rgt-neg-out_binary64_1743`
46×	`associate--l+_binary64_1720`
42×	`log-prod_binary64_1869`
38×	`swap-sqr_binary64_1750`
35×	`distribute-lft-neg-in_binary64_1740`
29×	`unpow3_binary64_1849`
28×	`unsub-neg_binary64_1777`
27×	`*-rgt-identity_binary64_1773` `distribute-rgt-out_binary64_1736`
26×	`*-lft-identity_binary64_1772`
17×	`pow-plus_binary64_1846`
16×	`cube-mult_binary64_1813`
15×	`associate--r+_binary64_1719`
12×	`prod-exp_binary64_1832`
11×	`distribute-lft-out_binary64_1734`
8×	`pow-sqr_binary64_1756` `distribute-rgt-out--_binary64_1737`
7×	`difference-of-squares_binary64_1752`
6×	`log-pow_binary64_1872` `exp-lft-sqr_binary64_1838`
4×	`unpow1/2_binary64_1847` `exp-diff_binary64_1831` `distribute-lft-out--_binary64_1735`
3×	`associate-+l-_binary64_1718` `associate-+r-_binary64_1717`
2×	`unpow2_binary64_1848` `unpow1_binary64_1841` `cube-unmult_binary64_1820` `count-2_binary64_1731`
1×	`1-exp_binary64_1827` `exp-1-e_binary64_1826` `div-sub_binary64_1788` `distribute-lft1-in_binary64_1738`
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-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `div-exp_binary64_1834` `rec-exp_binary64_1833` `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-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` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `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` `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` `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--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

139 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	4842
1	772	4515
2	3139	4497
3	4977	4497
4	4995	4497
5	4931	4497

prune256.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	120	3	123

Error

Counts

123 → 3

Compiler

Compiled 3608 to 2370 computations (34.3% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 a a) (+.f64 1 a))
0.2b	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)
0.8b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
25.5b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6))

rewrite234.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`pow1_binary64_1844` `add-exp-log_binary64_1821`
14×	`add-cbrt-cube_binary64_1819`
12×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
10×	`add-cube-cbrt_binary64_1818`
7×	`cbrt-prod_binary64_1814` `associate-r_binary64_1723`
6×	`unpow-prod-down_binary64_1862` `pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
4×	`add-log-exp_binary64_1822` `associate-*r/_binary64_1725`
3×	`distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `pow-unpow_binary64_1860`
2×	`sqr-pow_binary64_1755` `unswap-sqr_binary64_1751` `sub-neg_binary64_1776` `cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724` `*-commutative_binary64_1714`
1×	`pow1/3_binary64_1865` `flip3--_binary64_1787` `flip--_binary64_1758` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `flip3-+_binary64_1786` `flip-+_binary64_1757` `distribute-lft-out_binary64_1734`

Counts

4 → 81

Calls

4 calls:

9.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
7.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6))
5.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)

Compiler

Compiled 2994 to 1640 computations (45.2% saved)

series611.0ms (5.1%)

Error

Counts

4 → 38

Calls

4 calls:

296.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6))
148.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
68.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)
65.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 2384 to 1793 computations (24.8% saved)

simplify139.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

431×	`distribute-rgt-in_binary64_1733`
400×	`exp-prod_binary64_1835`
387×	`distribute-lft-in_binary64_1732`
344×	`*-commutative_binary64_1714`
225×	`log-prod_binary64_1869`
213×	`associate-l_binary64_1724`
204×	`+-commutative_binary64_1713`
168×	`associate-r_binary64_1723`
162×	`sqr-pow_binary64_1755`
139×	`cube-prod_binary64_1811`
130×	`unswap-sqr_binary64_1751`
120×	`distribute-rgt-neg-in_binary64_1741`
109×	`distribute-lft-neg-in_binary64_1740`
106×	`distribute-rgt-out_binary64_1736`
101×	`distribute-lft-neg-out_binary64_1742`
99×	`exp-sum_binary64_1829`
95×	`swap-sqr_binary64_1750` `distribute-rgt-neg-out_binary64_1743`
88×	`cancel-sign-sub-inv_binary64_1749`
67×	`log-pow_binary64_1872`
55×	`unpow3_binary64_1849`
50×	`pow-sqr_binary64_1756`
49×	`unsub-neg_binary64_1777`
48×	`neg-sub0_binary64_1778`
47×	`neg-mul-1_binary64_1779`
45×	`*-lft-identity_binary64_1772`
44×	`cube-mult_binary64_1813`
43×	`associate-/l*_binary64_1728`
40×	`*-rgt-identity_binary64_1773`
38×	`associate-+l+_binary64_1716`
36×	`associate-+r+_binary64_1715`
31×	`pow-plus_binary64_1846`
30×	`sub-neg_binary64_1776`
29×	`associate-+l-_binary64_1718`
26×	`cube-unmult_binary64_1820`
24×	`rem-sqrt-square_binary64_1796`
21×	`exp-diff_binary64_1831`
16×	`distribute-rgt1-in_binary64_1739` `distribute-lft-out_binary64_1734`
14×	`associate-/l/_binary64_1730` `associate-+r-_binary64_1717`
12×	`count-2_binary64_1731`
11×	`unpow1/2_binary64_1847`
9×	`associate-*r/_binary64_1725`
8×	`mul0-rgt_binary64_1766` `mul0-lft_binary64_1765`
7×	`exp-lft-cube_binary64_1839` `distribute-lft1-in_binary64_1738`
5×	`exp-neg_binary64_1830` `sub0-neg_binary64_1770`
4×	`unpow2_binary64_1848` `rem-cbrt-cube_binary64_1807` `sqr-neg_binary64_1797` `div-sub_binary64_1788` `distribute-rgt-out--_binary64_1737`
3×	`unpow1_binary64_1841` `difference-of-sqr-1_binary64_1753` `associate-/r/_binary64_1729` `associate-*l/_binary64_1726`
2×	`cube-neg_binary64_1810`
1×	`1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-3cbrt-lft_binary64_1808` `rem-cube-cbrt_binary64_1806` `+-rgt-identity_binary64_1768` `associate-/r*_binary64_1727`
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-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` `rem-exp-log_binary64_1823` `cube-div_binary64_1812` `rem-3cbrt-rft_binary64_1809` `sqr-abs_binary64_1798` `rem-square-sqrt_binary64_1795` `times-frac_binary64_1789` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `+-lft-identity_binary64_1767` `div0_binary64_1764` `*-inverses_binary64_1763` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `difference-of-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-lft-out--_binary64_1735` `associate--r-_binary64_1722` `associate--l-_binary64_1721` `associate--l+_binary64_1720` `associate--r+_binary64_1719`

Counts

119 → 94

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	158	1916
1	373	1748
2	1150	1717
3	2772	1681
4	4379	1624
5	4972	1624
6	4949	1624

prune136.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	94	3	97

Error

Counts

97 → 3

Compiler

Compiled 1974 to 1104 computations (44.1% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
1.1b	(.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))))
3.4b	(-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 8))
44.3b	(/.f64 (-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 8)) (-.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 4 a))))) (pow.f64 a 4)))

rewrite896.0ms (7.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

24×	`add-exp-log_binary64_1821`
20×	`add-sqr-sqrt_binary64_1805`
17×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
16×	`add-cbrt-cube_binary64_1819`
12×	`prod-exp_binary64_1832` `associate-*r/_binary64_1725`
10×	`distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732`
9×	`pow1_binary64_1844` `times-frac_binary64_1789` `cancel-sign-sub-inv_binary64_1749`
8×	`associate-l_binary64_1724`
7×	`unpow-prod-down_binary64_1862`
6×	`add-log-exp_binary64_1822` `cbrt-unprod_binary64_1816` `flip3-+_binary64_1786` `flip-+_binary64_1757`
4×	`flip3--_binary64_1787` `flip--_binary64_1758` `associate--l+_binary64_1720` `unswap-sqr_binary64_1751` `frac-times_binary64_1793` `associate-r_binary64_1723`
3×	`associate-/l_binary64_1728` `associate-/r_binary64_1727` `sub-neg_binary64_1776` `sqr-pow_binary64_1755` `pow-prod-down_binary64_1854`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `associate-l/_binary64_1726` `-commutative_binary64_1714`
1×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-sub_binary64_1788` `clear-num_binary64_1782` `div-inv_binary64_1780` `diff-log_binary64_1875`

Counts

4 → 118

Calls

4 calls:

46.0ms	(/.f64 (-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 8)) (-.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 4 a))))) (pow.f64 a 4)))
26.0ms	(-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 8))
25.0ms	(.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))))
8.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 10311 to 7009 computations (32% saved)

series2.1s (17.5%)

Error

Counts

4 → 35

Calls

4 calls:

1.6s	(/.f64 (-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 8)) (-.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 4 a))))) (pow.f64 a 4)))
193.0ms	(-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))))) (pow.f64 a 8))
117.0ms	(.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 4 a)))))
103.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 5365 to 4214 computations (21.5% saved)

simplify227.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

426×	`associate-l_binary64_1724`
413×	`associate-r_binary64_1723`
273×	`exp-prod_binary64_1835`
267×	`distribute-rgt-in_binary64_1733`
263×	`distribute-lft-in_binary64_1732`
237×	`*-commutative_binary64_1714`
133×	`associate-/l*_binary64_1728`
125×	`sub-neg_binary64_1776`
112×	`+-commutative_binary64_1713`
110×	`associate-+r+_binary64_1715`
92×	`log-prod_binary64_1869`
89×	`sqr-pow_binary64_1755`
88×	`times-frac_binary64_1789` `div-sub_binary64_1788`
78×	`associate-+l+_binary64_1716`
65×	`neg-mul-1_binary64_1779`
64×	`neg-sub0_binary64_1778`
62×	`cube-prod_binary64_1811` `associate-/r*_binary64_1727`
42×	`unswap-sqr_binary64_1751`
37×	`unpow3_binary64_1849`
34×	`associate-*l/_binary64_1726`
31×	`cancel-sign-sub-inv_binary64_1749` `associate-*r/_binary64_1725`
28×	`exp-sum_binary64_1829`
27×	`associate--l+_binary64_1720`
25×	`*-rgt-identity_binary64_1773`
24×	`distribute-rgt-neg-in_binary64_1741`
23×	`unsub-neg_binary64_1777` `associate--r+_binary64_1719`
22×	`associate-/r/_binary64_1729`
19×	`swap-sqr_binary64_1750` `distribute-lft-neg-in_binary64_1740`
18×	`*-lft-identity_binary64_1772`
17×	`associate-/l/_binary64_1730`
16×	`distribute-rgt-out_binary64_1736`
12×	`pow-plus_binary64_1846` `cube-mult_binary64_1813` `distribute-neg-in_binary64_1744` `distribute-lft-neg-out_binary64_1742`
11×	`log-pow_binary64_1872` `cube-unmult_binary64_1820` `pow-sqr_binary64_1756`
10×	`log-div_binary64_1870` `/-rgt-identity_binary64_1774`
7×	`unpow2_binary64_1848` `unpow1/2_binary64_1847` `unpow1_binary64_1841` `cube-div_binary64_1812`
6×	`+-rgt-identity_binary64_1768` `associate-+r-_binary64_1717`
5×	`exp-lft-sqr_binary64_1838` `exp-diff_binary64_1831` `rem-sqrt-square_binary64_1796` `difference-of-squares_binary64_1752` `distribute-rgt-neg-out_binary64_1743`
4×	`distribute-rgt-out--_binary64_1737` `distribute-lft-out_binary64_1734`
3×	`log-rec_binary64_1871`
2×	`rem-square-sqrt_binary64_1795` `remove-double-neg_binary64_1771` `count-2_binary64_1731` `associate--r-_binary64_1722`
1×	`div-exp_binary64_1834` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-3cbrt-lft_binary64_1808` `*-inverses_binary64_1763` `distribute-neg-frac_binary64_1747` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `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` `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` `exp-to-pow_binary64_1845` `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` `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-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `mul-1-neg_binary64_1775` `sub0-neg_binary64_1770` `--rgt-identity_binary64_1769` `+-lft-identity_binary64_1767` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `div0_binary64_1764` `+-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` `associate--l-_binary64_1721` `associate-+l-_binary64_1718`

Counts

153 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	359	7973
1	1024	7359
2	4267	7164
3	4700	7164
4	5004	7164

prune497.0ms (4.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	127	3	130

Error

Counts

130 → 3

Compiler

Compiled 7460 to 5086 computations (31.8% saved)

regimes1.6s (13.2%)

Accuracy

Total 0.0b remaining (60.7%)

Threshold costs 0.0b (60.7%)

Compiler

Compiled 23687 to 16999 computations (28.2% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	58
1	48	58
2	55	58
3	59	58
4	62	58
5	63	58
6	60	58

end2.0ms (0%)

Compiler: Compiled 39 to 28 computations (28.2% saved)

sample876.0ms (7.4%)

Algorithm

1×

intervals

Results

488.0ms	8000×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 208 to 157 computations (24.5% saved)

Details

analyze341.0ms (2.9%)

sample26.0ms (0.2%)

simplify67.0ms (0.6%)

prune4.0ms (0%)

localize19.0ms (0.2%)

rewrite238.0ms (2%)

series1.2s (9.8%)

simplify90.0ms (0.8%)

prune154.0ms (1.3%)

localize22.0ms (0.2%)

rewrite363.0ms (3.1%)

series1.6s (13.6%)

simplify197.0ms (1.7%)

prune256.0ms (2.2%)

localize21.0ms (0.2%)

rewrite234.0ms (2%)

series611.0ms (5.1%)

simplify139.0ms (1.2%)

prune136.0ms (1.1%)

localize30.0ms (0.3%)

rewrite896.0ms (7.5%)

series2.1s (17.5%)

simplify227.0ms (1.9%)

prune497.0ms (4.2%)

regimes1.6s (13.2%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end2.0ms (0%)

sample876.0ms (7.4%)

Profiling