Details

analyze53.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Compiler

Compiled 63 to 34 computations (46% saved)

sample51.0ms (0.2%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify81.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

723×	`associate-+l+_binary64_1716`
490×	`associate-l_binary64_1724`
418×	`associate-r_binary64_1723`
369×	`times-frac_binary64_1789`
335×	`associate-/l*_binary64_1728`
252×	`distribute-rgt-in_binary64_1733`
250×	`distribute-lft-in_binary64_1732`
165×	`associate-/l/_binary64_1730`
164×	`associate-/r*_binary64_1727`
153×	`associate-*l/_binary64_1726`
130×	`associate-*r/_binary64_1725`
95×	`associate-/r/_binary64_1729`
75×	`associate--l+_binary64_1720`
49×	`*-commutative_binary64_1714`
47×	`associate-+r+_binary64_1715`
38×	`div-sub_binary64_1788`
32×	`distribute-rgt-out_binary64_1736`
24×	`+-commutative_binary64_1713`
20×	`associate--r+_binary64_1719`
19×	`associate-+r-_binary64_1717`
15×	`distribute-lft-out_binary64_1734`
12×	`sub-neg_binary64_1776`
9×	`unsub-neg_binary64_1777` `associate-+l-_binary64_1718`
8×	`swap-sqr_binary64_1750`
5×	`distribute-rgt-neg-out_binary64_1743`
4×	`mul-1-neg_binary64_1775` `distribute-lft-neg-out_binary64_1742`
3×	`+-rgt-identity_binary64_1768`
2×	`*-rgt-identity_binary64_1773`
1×	`1-exp_binary64_1827` `cube-unmult_binary64_1820` `neg-mul-1_binary64_1779` `neg-sub0_binary64_1778` `*-lft-identity_binary64_1772` `sub0-neg_binary64_1770` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `cancel-sign-sub-inv_binary64_1749`
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-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` `/-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` `pow-sqr_binary64_1756` `sqr-pow_binary64_1755` `difference-of-squares_binary64_1752` `unswap-sqr_binary64_1751` `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-in_binary64_1741` `distribute-lft-neg-in_binary64_1740` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `distribute-rgt-out--_binary64_1737` `distribute-lft-out--_binary64_1735` `count-2_binary64_1731` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

1 → 4

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	79
1	64	79
2	286	79
3	1600	79

prune12.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1	3	4
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	3	5

Error

42.8b

Counts

5 → 3

Compiler

Compiled 371 to 205 computations (44.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (*.f64 i 2))))
0.1b	(.f64 (/.f64 (+.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 alpha beta)) (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (.f64 i 2)))) 1)) (/.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (.f64 i 2))))))
43.0b	(/.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (.f64 i 2)))))
43.0b	(/.f64 (+.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 alpha beta)) (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (*.f64 i 2)))) 1))

rewrite435.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

42.8b

Rules

61×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
51×	`*-un-lft-identity_binary64_1783`
44×	`add-sqr-sqrt_binary64_1805`
39×	`times-frac_binary64_1789`
30×	`add-cube-cbrt_binary64_1818`
28×	`associate-l_binary64_1724`
23×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
20×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-/r/_binary64_1729`
18×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
17×	`associate-r_binary64_1723`
14×	`difference-of-squares_binary64_1752`
13×	`pow1_binary64_1844` `frac-times_binary64_1793`
9×	`associate-*r/_binary64_1725`
7×	`difference-of-sqr-1_binary64_1753` `associate-/r_binary64_1727` `associate-l/_binary64_1726`
6×	`swap-sqr_binary64_1750` `distribute-lft-out_binary64_1734`
4×	`add-log-exp_binary64_1822` `div-inv_binary64_1780` `associate-/l/_binary64_1730` `associate-/l*_binary64_1728`
3×	`unswap-sqr_binary64_1751`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `flip3--_binary64_1787` `flip--_binary64_1758` `pow-prod-down_binary64_1854` `*-commutative_binary64_1714`
1×	`pow2_binary64_1864` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846` `pow-sqr_binary64_1756` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732`

Counts

4 → 185

Calls

4 calls:

40.0ms	(.f64 (/.f64 (+.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 alpha beta)) (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (.f64 i 2)))) 1)) (/.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (.f64 i 2))))))
19.0ms	(/.f64 (+.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 alpha beta)) (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (*.f64 i 2)))) 1))
16.0ms	(/.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (.f64 i 2)))))
9.0ms	(.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (*.f64 i 2))))

Compiler

Compiled 14526 to 6609 computations (54.5% saved)

series6.1s (23.4%)

Error

9.2b

Counts

4 → 76

Calls

4 calls:

5.4s	(.f64 (/.f64 (+.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 alpha beta)) (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (.f64 i 2)))) 1)) (/.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (.f64 i 2))))))
268.0ms	(/.f64 (+.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 alpha beta)) (-.f64 (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (*.f64 i 2)))) 1))
158.0ms	(/.f64 (.f64 i (+.f64 beta (+.f64 alpha i))) (.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (.f64 i 2)))))
130.0ms	(.f64 (+.f64 alpha (+.f64 beta (.f64 i 2))) (+.f64 alpha (+.f64 beta (*.f64 i 2))))

Compiler

Compiled 25080 to 17285 computations (31.1% saved)

simplify3.7s (14.1%)

Algorithm

1×	egg-herbie

Rules

333×	`distribute-rgt-in_binary64_1733`
315×	`distribute-lft-in_binary64_1732`
242×	`*-commutative_binary64_1714`
162×	`+-commutative_binary64_1713`
132×	`associate-*r/_binary64_1725`
116×	`associate-+r+_binary64_1715`
115×	`associate-/l*_binary64_1728`
100×	`unswap-sqr_binary64_1751`
99×	`sub-neg_binary64_1776`
98×	`associate-/r*_binary64_1727`
92×	`times-frac_binary64_1789`
73×	`cancel-sign-sub-inv_binary64_1749`
71×	`sqr-pow_binary64_1755`
60×	`associate-r_binary64_1723`
56×	`distribute-neg-in_binary64_1744`
47×	`associate-/l/_binary64_1730`
35×	`associate-*l/_binary64_1726`
33×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
27×	`pow-sqr_binary64_1756`
26×	`distribute-rgt-neg-in_binary64_1741`
25×	`distribute-rgt-out_binary64_1736`
21×	`associate-l_binary64_1724`
20×	`distribute-lft-neg-in_binary64_1740`
18×	`associate--l+_binary64_1720`
17×	`associate--r+_binary64_1719`
15×	`swap-sqr_binary64_1750`
14×	`distribute-lft-out_binary64_1734`
12×	`log-prod_binary64_1869`
11×	`exp-prod_binary64_1835`
9×	`unpow2_binary64_1848` `cube-unmult_binary64_1820` `*-rgt-identity_binary64_1773`
8×	`log-div_binary64_1870` `unpow3_binary64_1849`
7×	`cube-mult_binary64_1813`
6×	`pow-plus_binary64_1846` `cube-prod_binary64_1811` `distribute-rgt-out--_binary64_1737`
5×	`div-sub_binary64_1788` `difference-of-squares_binary64_1752` `distribute-lft-neg-out_binary64_1742`
4×	`exp-sum_binary64_1829` `/-rgt-identity_binary64_1774` `difference-of-sqr-1_binary64_1753` `associate-+r-_binary64_1717`
3×	`rem-sqrt-square_binary64_1796`
2×	`pow-base-1_binary64_1843` `distribute-neg-frac_binary64_1747` `distribute-rgt1-in_binary64_1739` `count-2_binary64_1731` `associate-+l+_binary64_1716`
1×	`div-exp_binary64_1834` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `1-exp_binary64_1827` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-square-sqrt_binary64_1795` `unsub-neg_binary64_1777` `-lft-identity_binary64_1772` `-inverses_binary64_1763` `associate-+l-_binary64_1718`
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` `pow-base-0_binary64_1867` `unpow1/3_binary64_1850` `unpow1/2_binary64_1847` `exp-to-pow_binary64_1845` `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-diff_binary64_1831` `exp-neg_binary64_1830` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-div_binary64_1812` `cube-neg_binary64_1810` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `mul-1-neg_binary64_1775` `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_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `cancel-sign-sub_binary64_1748` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-rgt-neg-out_binary64_1743` `distribute-lft1-in_binary64_1738` `distribute-lft-out--_binary64_1735` `associate-/r/_binary64_1729` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

261 → 603

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	784	19475
1	2801	17422

prune5.5s (20.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	597	6	603
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	599	7	606

Error

12.2b

Counts

606 → 7

Compiler

Compiled 50885 to 22000 computations (56.8% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1/64 (.f64 i i)) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)))))
0.7b	(/.f64 1/64 (*.f64 i i))
10.2b	(/.f64 (.f64 beta beta) (.f64 i i))
12.5b	(/.f64 (.f64 alpha alpha) (.f64 i i))

rewrite757.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

6.1b

Rules

33×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
10×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
9×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
6×	`add-log-exp_binary64_1822` `add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
5×	`times-frac_binary64_1789` `associate-/l*_binary64_1728`
4×	`pow1_binary64_1844`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `associate-/r_binary64_1727` `associate-r/_binary64_1725` `frac-sub_binary64_1792`
2×	`associate--r+_binary64_1719`
1×	`diff-log_binary64_1875` `frac-add_binary64_1791` `flip3-+_binary64_1786` `flip-+_binary64_1757` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `cancel-sign-sub-inv_binary64_1749` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732`

Counts

4 → 80

Calls

4 calls:

29.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
7.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
6.0ms	(-.f64 (/.f64 1/64 (.f64 i i)) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)))))
3.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 2840 to 914 computations (67.8% saved)

series1.1s (4.4%)

Error

6.1b

Counts

4 → 27

Calls

4 calls:

645.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
318.0ms	(-.f64 (/.f64 1/64 (.f64 i i)) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)))))
102.0ms	(/.f64 1/64 (*.f64 i i))
52.0ms	(/.f64 (.f64 beta beta) (.f64 i i))

Compiler

Compiled 1808 to 1387 computations (23.3% saved)

simplify345.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

435×	`distribute-rgt-in_binary64_1733`
420×	`distribute-lft-in_binary64_1732`
306×	`times-frac_binary64_1789`
274×	`associate-/l/_binary64_1730`
221×	`cancel-sign-sub-inv_binary64_1749`
162×	`distribute-rgt-neg-in_binary64_1741`
150×	`associate-/l_binary64_1728` `associate-r*_binary64_1723`
141×	`associate-l_binary64_1724`
138×	`distribute-lft-neg-in_binary64_1740`
135×	`associate-/r*_binary64_1727`
116×	`unswap-sqr_binary64_1751`
88×	`associate-*l/_binary64_1726`
76×	`*-commutative_binary64_1714`
72×	`associate-*r/_binary64_1725`
71×	`sub-neg_binary64_1776`
69×	`distribute-neg-frac_binary64_1747`
61×	`distribute-neg-in_binary64_1744`
59×	`sqr-pow_binary64_1755`
56×	`distribute-lft-neg-out_binary64_1742`
52×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
35×	`log-div_binary64_1870`
33×	`distribute-rgt-out_binary64_1736`
32×	`pow-sqr_binary64_1756`
29×	`log-prod_binary64_1869` `+-commutative_binary64_1713`
28×	`exp-prod_binary64_1835`
27×	`distribute-rgt-neg-out_binary64_1743`
21×	`cube-prod_binary64_1811`
20×	`cube-div_binary64_1812`
19×	`unpow3_binary64_1849`
18×	`pow-plus_binary64_1846`
17×	`associate-/r/_binary64_1729`
14×	`distribute-lft-out_binary64_1734`
13×	`swap-sqr_binary64_1750`
12×	`exp-sum_binary64_1829` `distribute-rgt-out--_binary64_1737`
11×	`div-sub_binary64_1788` `associate--r+_binary64_1719`
10×	`difference-of-squares_binary64_1752`
9×	`cube-mult_binary64_1813`
7×	`distribute-lft-out--_binary64_1735` `associate--l+_binary64_1720` `associate-+l+_binary64_1716`
6×	`log-pow_binary64_1872` `exp-diff_binary64_1831` `unsub-neg_binary64_1777`
5×	`cube-unmult_binary64_1820`
4×	`associate-+r+_binary64_1715`
3×	`unpow2_binary64_1848` `unpow1_binary64_1841` `count-2_binary64_1731`
2×	`rem-sqrt-square_binary64_1796` `*-rgt-identity_binary64_1773` `associate-+r-_binary64_1717`
1×	`div-exp_binary64_1834` `1-exp_binary64_1827` `/-rgt-identity_binary64_1774` `+-rgt-identity_binary64_1768` `*-inverses_binary64_1763` `associate-+l-_binary64_1718`
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` `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` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-lft-sqr_binary64_1838` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `exp-neg_binary64_1830` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-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` `mul-1-neg_binary64_1775` `*-lft-identity_binary64_1772` `remove-double-neg_binary64_1771` `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` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

107 → 247

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	2127
1	526	1970
2	2462	1740

prune201.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	247	7	254

Error

6.1b

Counts

254 → 7

Compiler

Compiled 10058 to 3382 computations (66.4% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 (.f64 (/.f64 beta i) (/.f64 beta i)) -1/32)
0.1b	(*.f64 (/.f64 beta i) (/.f64 beta i))

rewrite72.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

6.1b

Rules

44×	`add-sqr-sqrt_binary64_1805`
40×	`times-frac_binary64_1789`
32×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
31×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
16×	`associate-r_binary64_1723`
14×	`pow1_binary64_1844` `associate-l_binary64_1724`
13×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `swap-sqr_binary64_1750`
8×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
5×	`unswap-sqr_binary64_1751` `associate-*l/_binary64_1726`
4×	`pow-prod-down_binary64_1854` `div-inv_binary64_1780`
2×	`add-log-exp_binary64_1822` `frac-times_binary64_1793` `associate-r/_binary64_1725` `-commutative_binary64_1714`
1×	`pow2_binary64_1864` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846` `pow-sqr_binary64_1756`

Counts

2 → 95

Calls

2 calls:

11.0ms	(*.f64 (/.f64 beta i) (/.f64 beta i))
8.0ms	(.f64 (.f64 (/.f64 beta i) (/.f64 beta i)) -1/32)

Compiler

Compiled 1848 to 700 computations (62.1% saved)

series102.0ms (0.4%)

Error

6.1b

Counts

2 → 12

Calls

2 calls:

55.0ms	(*.f64 (/.f64 beta i) (/.f64 beta i))
41.0ms	(.f64 (.f64 (/.f64 beta i) (/.f64 beta i)) -1/32)

Compiler

Compiled 396 to 399 computations (-0.8% saved)

simplify571.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

533×	`associate-/l/_binary64_1730`
498×	`unswap-sqr_binary64_1751`
305×	`associate-/r*_binary64_1727`
286×	`distribute-rgt-in_binary64_1733`
261×	`*-commutative_binary64_1714`
260×	`associate-/r/_binary64_1729`
181×	`associate-l_binary64_1724`
174×	`associate-*l/_binary64_1726`
147×	`log-div_binary64_1870`
145×	`cube-div_binary64_1812`
142×	`log-prod_binary64_1869`
139×	`associate-r_binary64_1723`
135×	`associate-*r/_binary64_1725`
125×	`swap-sqr_binary64_1750`
121×	`associate-/l*_binary64_1728`
115×	`cube-prod_binary64_1811`
104×	`exp-prod_binary64_1835`
103×	`sqr-pow_binary64_1755`
85×	`*-lft-identity_binary64_1772`
67×	`*-rgt-identity_binary64_1773`
57×	`cancel-sign-sub-inv_binary64_1749`
47×	`times-frac_binary64_1789`
39×	`pow-sqr_binary64_1756`
37×	`sub-neg_binary64_1776`
30×	`distribute-neg-in_binary64_1744`
28×	`associate-+l+_binary64_1716`
27×	`associate-+r+_binary64_1715`
22×	`unpow3_binary64_1849` `distribute-rgt-out_binary64_1736`
20×	`cube-mult_binary64_1813` `distribute-lft-in_binary64_1732`
19×	`pow-plus_binary64_1846`
17×	`unsub-neg_binary64_1777`
16×	`div-exp_binary64_1834` `prod-exp_binary64_1832` `neg-mul-1_binary64_1779`
15×	`cube-unmult_binary64_1820` `associate-+l-_binary64_1718`
13×	`exp-sqrt_binary64_1836` `neg-sub0_binary64_1778`
12×	`log-pow_binary64_1872` `exp-lft-sqr_binary64_1838` `/-rgt-identity_binary64_1774` `+-commutative_binary64_1713`
10×	`distribute-lft-neg-in_binary64_1740` `distribute-rgt-out--_binary64_1737` `associate-+r-_binary64_1717`
9×	`log-rec_binary64_1871` `rem-sqrt-square_binary64_1796` `associate--r+_binary64_1719`
8×	`distribute-lft-neg-out_binary64_1742`
7×	`distribute-rgt1-in_binary64_1739`
6×	`distribute-rgt-neg-out_binary64_1743` `distribute-rgt-neg-in_binary64_1741` `associate--r-_binary64_1722`
5×	`distribute-lft-out_binary64_1734` `associate--l+_binary64_1720`
4×	`rec-exp_binary64_1833` `count-2_binary64_1731`
3×	`exp-sum_binary64_1829` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-square-sqrt_binary64_1795` `associate--l-_binary64_1721`
2×	`unpow2_binary64_1848` `unpow1_binary64_1841` `distribute-neg-out_binary64_1745` `distribute-lft1-in_binary64_1738` `distribute-lft-out--_binary64_1735`
1×	`pow-base-1_binary64_1843` `exp-diff_binary64_1831` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-log-exp_binary64_1824` `remove-double-neg_binary64_1771` `+-rgt-identity_binary64_1768` `mul0-lft_binary64_1765` `*-inverses_binary64_1763` `remove-double-div_binary64_1759`
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` `unpow1/2_binary64_1847` `exp-to-pow_binary64_1845` `unpow0_binary64_1842` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-cbrt_binary64_1837` `exp-neg_binary64_1830` `e-exp-1_binary64_1828` `exp-0_binary64_1825` `rem-exp-log_binary64_1823` `cube-neg_binary64_1810` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `div-sub_binary64_1788` `mul-1-neg_binary64_1775` `sub0-neg_binary64_1770` `--rgt-identity_binary64_1769` `+-lft-identity_binary64_1767` `mul0-rgt_binary64_1766` `div0_binary64_1764` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `difference-of-squares_binary64_1752` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746`

Counts

107 → 239

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	1845
1	392	1492
2	1407	1412
3	3211	1327

prune125.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	237	2	239
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	239	7	246

Error

6.1b

Counts

246 → 7

Compiler

Compiled 4607 to 1815 computations (60.6% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 (.f64 beta (/.f64 beta (*.f64 i i))) -1/32)
3.1b	(.f64 beta (/.f64 beta (.f64 i i)))
4.2b	(/.f64 beta (*.f64 i i))

rewrite77.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

6.1b

Rules

31×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
13×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `add-sqr-sqrt_binary64_1805`
10×	`pow1_binary64_1844` `associate-r_binary64_1723`
9×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
7×	`times-frac_binary64_1789`
6×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
4×	`pow-prod-down_binary64_1854` `associate-l_binary64_1724`
3×	`add-log-exp_binary64_1822` `associate-/l*_binary64_1728`
2×	`div-inv_binary64_1780` `unswap-sqr_binary64_1751` `associate-r/_binary64_1725` `-commutative_binary64_1714`
1×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-/r_binary64_1727` `associate-l/_binary64_1726`

Counts

3 → 72

Calls

3 calls:

28.0ms	(/.f64 beta (*.f64 i i))
6.0ms	(.f64 (.f64 beta (/.f64 beta (*.f64 i i))) -1/32)
6.0ms	(.f64 beta (/.f64 beta (.f64 i i)))

Compiler

Compiled 1276 to 513 computations (59.8% saved)

series161.0ms (0.6%)

Error

6.1b

Counts

3 → 18

Calls

3 calls:

76.0ms	(.f64 (.f64 beta (/.f64 beta (*.f64 i i))) -1/32)
43.0ms	(.f64 beta (/.f64 beta (.f64 i i)))
35.0ms	(/.f64 beta (*.f64 i i))

Compiler

Compiled 594 to 579 computations (2.5% saved)

simplify468.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

408×	`unswap-sqr_binary64_1751`
358×	`associate-/l*_binary64_1728`
310×	`*-commutative_binary64_1714`
257×	`sqr-pow_binary64_1755`
230×	`associate-/r*_binary64_1727`
216×	`sub-neg_binary64_1776`
178×	`cancel-sign-sub-inv_binary64_1749`
154×	`associate-l_binary64_1724`
143×	`log-div_binary64_1870`
129×	`cube-div_binary64_1812`
127×	`log-prod_binary64_1869`
116×	`distribute-rgt-in_binary64_1733`
113×	`pow-sqr_binary64_1756`
109×	`associate-r_binary64_1723`
108×	`swap-sqr_binary64_1750`
101×	`cube-prod_binary64_1811`
93×	`exp-prod_binary64_1835`
87×	`associate-+l+_binary64_1716`
84×	`times-frac_binary64_1789`
82×	`associate-/r/_binary64_1729`
70×	`associate-/l/_binary64_1730` `associate-+l-_binary64_1718`
56×	`distribute-neg-in_binary64_1744` `associate-+r+_binary64_1715`
55×	`unpow3_binary64_1849`
50×	`cube-mult_binary64_1813`
49×	`unsub-neg_binary64_1777`
45×	`neg-mul-1_binary64_1779` `associate-l/_binary64_1726` `associate-r/_binary64_1725`
42×	`associate--l+_binary64_1720`
41×	`*-lft-identity_binary64_1772`
39×	`pow-plus_binary64_1846` `*-rgt-identity_binary64_1773` `associate-+r-_binary64_1717`
35×	`distribute-rgt-neg-in_binary64_1741`
33×	`distribute-lft-neg-in_binary64_1740`
32×	`neg-sub0_binary64_1778`
29×	`associate--r+_binary64_1719`
27×	`distribute-rgt-out_binary64_1736`
26×	`+-commutative_binary64_1713`
25×	`associate--l-_binary64_1721`
16×	`cube-unmult_binary64_1820`
15×	`log-pow_binary64_1872` `div-sub_binary64_1788`
13×	`log-rec_binary64_1871`
12×	`/-rgt-identity_binary64_1774`
11×	`distribute-neg-out_binary64_1745` `distribute-lft-neg-out_binary64_1742` `distribute-lft-out--_binary64_1735` `distribute-lft-in_binary64_1732`
10×	`rem-sqrt-square_binary64_1796` `distribute-neg-frac_binary64_1747` `distribute-rgt1-in_binary64_1739`
8×	`sub0-neg_binary64_1770`
7×	`distribute-rgt-neg-out_binary64_1743` `distribute-rgt-out--_binary64_1737`
6×	`count-2_binary64_1731`
5×	`distribute-lft-out_binary64_1734`
4×	`remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `associate--r-_binary64_1722`
3×	`exp-sum_binary64_1829`
2×	`unpow2_binary64_1848` `exp-to-pow_binary64_1845` `unpow1_binary64_1841` `exp-lft-sqr_binary64_1838` `+-rgt-identity_binary64_1768` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `distribute-lft1-in_binary64_1738`
1×	`pow-base-1_binary64_1843` `exp-sqrt_binary64_1836` `prod-exp_binary64_1832` `exp-diff_binary64_1831` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `rem-square-sqrt_binary64_1795` `div0_binary64_1764` `*-inverses_binary64_1763` `rgt-mult-inverse_binary64_1760` `cancel-sign-sub_binary64_1748`
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` `unpow1/2_binary64_1847` `unpow0_binary64_1842` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-cbrt_binary64_1837` `div-exp_binary64_1834` `rec-exp_binary64_1833` `exp-neg_binary64_1830` `e-exp-1_binary64_1828` `exp-0_binary64_1825` `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` `mul-1-neg_binary64_1775` `+-lft-identity_binary64_1767` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `difference-of-squares_binary64_1752` `distribute-frac-neg_binary64_1746`

Counts

90 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1306
1	232	1042
2	995	1013
3	2129	1001
4	3741	1001

prune99.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	216	7	223

Error

6.1b

Counts

223 → 7

Compiler

Compiled 3641 to 1594 computations (56.2% saved)

regimes986.0ms (3.8%)

Accuracy

Total 2.8b remaining (25.6%)

Threshold costs 0b (0%)

Compiler

Compiled 17964 to 11097 computations (38.2% saved)

bsearch45.0ms (0.2%)

Steps

Iters	Range		Point
7	4.3124762736737256e+145	3.2659851577817696e+147	8.623959790867124e+146

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64_1713`
7×	`*-commutative_binary64_1714`
2×	`sub-neg_binary64_1776`
1×	`1-exp_binary64_1827` `neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `unpow1_binary64_1841` `e-exp-1_binary64_1828` `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	36	115
1	50	115
2	54	115
3	56	115
4	57	115

Proof

(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h2 h0))) (* f64 h2 h1))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h1 h2) (* f64 h0 (+ f64 h1 (+ f64 h2 h0))))) (* f64 (/ f64 h0 (+ f64 (+ f64 h1 h2) (* f64 2 h0))) (/ f64 (+ f64 h1 (+ f64 h2 h0)) (+ f64 (+ f64 h1 h2) (* f64 2 h0))))) (- f64 (+ f64 (+ f64 h1 h2) (* f64 2 h0)) (sqrt f64 1)))) 1/16)
<= *-commutative_binary64_1714
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h2 h0))) (=> (* f64 h2 h1)))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (<= (* f64 h2 h1)) (* f64 h0 (+ f64 h1 (+ f64 h2 h0))))) (* f64 (/ f64 h0 (+ f64 (+ f64 h1 h2) (* f64 2 h0))) (/ f64 (+ f64 h1 (+ f64 h2 h0)) (+ f64 (+ f64 h1 h2) (* f64 2 h0))))) (- f64 (+ f64 (+ f64 h1 h2) (* f64 2 h0)) (sqrt f64 1)))) 1/16)
*-commutative_binary64_1714 =>
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h2 h0))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h2 h1) (* f64 h0 (+ f64 h1 (+ f64 h2 h0))))) (* f64 (/ f64 h0 (+ f64 (+ f64 h1 h2) (* f64 2 h0))) (/ f64 (+ f64 h1 (+ f64 h2 h0)) (+ f64 (+ f64 h1 h2) (* f64 2 h0))))) (- f64 (=> (+ f64 (+ f64 h1 h2) (* f64 2 h0))) (sqrt f64 1)))) 1/16)
+-commutative_binary64_1713 =>
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h2 h0))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h2 h1) (* f64 h0 (+ f64 h1 (+ f64 h2 h0))))) (* f64 (/ f64 h0 (+ f64 (+ f64 h1 h2) (* f64 2 h0))) (/ f64 (+ f64 h1 (+ f64 h2 h0)) (+ f64 (+ f64 h1 h2) (* f64 2 h0))))) (- f64 (+ f64 (* f64 2 h0) (+ f64 h1 h2)) (sqrt f64 1)))) 1/16)
<= *-commutative_binary64_1714
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h2 h0))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h2 h1) (* f64 h0 (+ f64 h1 (+ f64 h2 h0))))) (* f64 (/ f64 h0 (+ f64 (+ f64 h1 h2) (* f64 2 h0))) (/ f64 (+ f64 h1 (+ f64 h2 h0)) (=> (+ f64 (+ f64 h1 h2) (* f64 2 h0)))))) (- f64 (+ f64 (<= (* f64 h0 2)) (+ f64 h1 h2)) (sqrt f64 1)))) 1/16)
+-commutative_binary64_1713 =>
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h2 h0))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h2 h1) (* f64 h0 (+ f64 h1 (+ f64 h2 h0))))) (* f64 (/ f64 h0 (+ f64 (+ f64 h1 h2) (* f64 2 h0))) (/ f64 (+ f64 h1 (+ f64 h2 h0)) (+ f64 (* f64 2 h0) (+ f64 h1 h2))))) (- f64 (+ f64 (* f64 h0 2) (+ f64 h1 h2)) (sqrt f64 1)))) 1/16)
<= *-commutative_binary64_1714
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h2 h0))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h2 h1) (* f64 h0 (+ f64 h1 (+ f64 h2 h0))))) (* f64 (/ f64 h0 (=> (+ f64 (+ f64 h1 h2) (* f64 2 h0)))) (/ f64 (+ f64 h1 (+ f64 h2 h0)) (+ f64 (<= (* f64 h0 2)) (+ f64 h1 h2))))) (- f64 (+ f64 (* f64 h0 2) (+ f64 h1 h2)) (sqrt f64 1)))) 1/16)
+-commutative_binary64_1713 =>
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h2 h0))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h2 h1) (* f64 h0 (+ f64 h1 (+ f64 h2 h0))))) (* f64 (/ f64 h0 (+ f64 (* f64 2 h0) (+ f64 h1 h2))) (/ f64 (+ f64 h1 (+ f64 h2 h0)) (+ f64 (* f64 h0 2) (+ f64 h1 h2))))) (- f64 (+ f64 (* f64 h0 2) (+ f64 h1 h2)) (sqrt f64 1)))) 1/16)
<= *-commutative_binary64_1714
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h2 h0))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h2 h1) (* f64 h0 (+ f64 h1 (+ f64 h2 h0))))) (* f64 (/ f64 h0 (+ f64 (<= (* f64 h0 2)) (+ f64 h1 h2))) (/ f64 (+ f64 h1 (=> (+ f64 h2 h0))) (+ f64 (* f64 h0 2) (+ f64 h1 h2))))) (- f64 (+ f64 (* f64 h0 2) (+ f64 h1 h2)) (sqrt f64 1)))) 1/16)
+-commutative_binary64_1713 =>
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (=> (+ f64 h2 h0)))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h2 h1) (* f64 h0 (+ f64 h1 (+ f64 h2 h0))))) (* f64 (/ f64 h0 (+ f64 (* f64 h0 2) (+ f64 h1 h2))) (/ f64 (+ f64 h1 (+ f64 h0 h2)) (+ f64 (* f64 h0 2) (+ f64 h1 h2))))) (- f64 (+ f64 (* f64 h0 2) (+ f64 h1 h2)) (sqrt f64 1)))) 1/16)
+-commutative_binary64_1713 =>
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h0 h2))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h2 h1) (* f64 h0 (+ f64 h1 (+ f64 h2 h0))))) (* f64 (/ f64 h0 (+ f64 (* f64 h0 2) (+ f64 h1 h2))) (/ f64 (+ f64 h1 (+ f64 h0 h2)) (+ f64 (* f64 h0 2) (+ f64 h1 h2))))) (- f64 (+ f64 (* f64 h0 2) (+ f64 h1 h2)) (sqrt f64 1)))) 1/16)
<= +-commutative_binary64_1713
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h0 h2))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (<= (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h2 h0))) (=> (* f64 h2 h1))))) (* f64 (/ f64 h0 (+ f64 (* f64 h0 2) (+ f64 h1 h2))) (/ f64 (+ f64 h1 (+ f64 h0 h2)) (+ f64 (* f64 h0 2) (+ f64 h1 h2))))) (- f64 (+ f64 (* f64 h0 2) (+ f64 h1 h2)) (sqrt f64 1)))) 1/16)
*-commutative_binary64_1714 =>
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h0 h2))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (=> (+ f64 h2 h0)))) (* f64 h1 h2))) (* f64 (/ f64 h0 (+ f64 (* f64 h0 2) (+ f64 h1 h2))) (/ f64 (+ f64 h1 (+ f64 h0 h2)) (+ f64 (* f64 h0 2) (+ f64 h1 h2))))) (- f64 (+ f64 (* f64 h0 2) (+ f64 h1 h2)) (sqrt f64 1)))) 1/16)
+-commutative_binary64_1713 =>
(if real (<= f64 h0 862395979086712392463990855648827521156587659081658088192386140713949835015336886683213933306258611069656866174989145505411902015675110530698182656) (* f64 (/ f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h0 h2))) (* f64 h1 h2))) (+ f64 (+ f64 h2 (+ f64 h1 (* f64 h0 2))) (sqrt f64 1))) (/ f64 (* f64 (sqrt f64 (+ f64 (* f64 h0 (+ f64 h1 (+ f64 h0 h2))) (* f64 h1 h2))) (* f64 (/ f64 h0 (+ f64 (* f64 h0 2) (+ f64 h1 h2))) (/ f64 (+ f64 h1 (+ f64 h0 h2)) (+ f64 (* f64 h0 2) (+ f64 h1 h2))))) (- f64 (+ f64 (* f64 h0 2) (+ f64 h1 h2)) (sqrt f64 1)))) 1/16)

end0.0ms (0%)

sample5.0s (19.2%)

Algorithm

1×

intervals

Results

951.0ms	8000×	body	128	valid
218.0ms	8000×	pre	128	true

Compiler

Compiled 4562 to 2812 computations (38.4% saved)

Details

analyze53.0ms (0.2%)

sample51.0ms (0.2%)

simplify81.0ms (0.3%)

prune12.0ms (0%)

localize16.0ms (0.1%)

rewrite435.0ms (1.7%)

series6.1s (23.4%)

simplify3.7s (14.1%)

prune5.5s (20.9%)

localize13.0ms (0%)

rewrite757.0ms (2.9%)

series1.1s (4.4%)

simplify345.0ms (1.3%)

prune201.0ms (0.8%)

localize6.0ms (0%)

rewrite72.0ms (0.3%)

series102.0ms (0.4%)

simplify571.0ms (2.2%)

prune125.0ms (0.5%)

localize7.0ms (0%)

rewrite77.0ms (0.3%)

series161.0ms (0.6%)

simplify468.0ms (1.8%)

prune99.0ms (0.4%)

regimes986.0ms (3.8%)

bsearch45.0ms (0.2%)

simplify18.0ms (0.1%)

end0.0ms (0%)

sample5.0s (19.2%)

Profiling