Details

analyze73.0ms (1.1%)

Algorithm

1×

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%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample19.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify154.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

600×	`unswap-sqr_binary64_1751`
497×	`sub-neg_binary64_1776`
479×	`cancel-sign-sub-inv_binary64_1749`
416×	`associate-l_binary64_1724`
376×	`associate-r_binary64_1723`
282×	`associate-+l+_binary64_1716`
248×	`associate-+r+_binary64_1715`
240×	`distribute-rgt-in_binary64_1733`
233×	`distribute-neg-in_binary64_1744`
195×	`distribute-lft-in_binary64_1732`
179×	`associate--r+_binary64_1719`
174×	`associate--l+_binary64_1720`
168×	`unsub-neg_binary64_1777`
167×	`distribute-rgt-neg-in_binary64_1741`
147×	`+-commutative_binary64_1713`
139×	`distribute-lft-neg-in_binary64_1740`
124×	`associate-+l-_binary64_1718`
122×	`*-commutative_binary64_1714`
114×	`neg-mul-1_binary64_1779`
112×	`neg-sub0_binary64_1778`
98×	`associate--r-_binary64_1722`
58×	`distribute-lft-out_binary64_1734`
50×	`associate--l-_binary64_1721`
43×	`distribute-rgt-out_binary64_1736`
38×	`sqr-pow_binary64_1755`
37×	`associate-+r-_binary64_1717`
29×	`distribute-lft-neg-out_binary64_1742`
24×	`remove-double-neg_binary64_1771` `+-rgt-identity_binary64_1768`
21×	`pow-sqr_binary64_1756`
19×	`pow-plus_binary64_1846`
14×	`+-lft-identity_binary64_1767` `difference-of-sqr--1_binary64_1754`
11×	`*-rgt-identity_binary64_1773` `sub0-neg_binary64_1770`
10×	`cube-prod_binary64_1811` `--rgt-identity_binary64_1769`
9×	`*-lft-identity_binary64_1772` `associate-/l/_binary64_1730`
8×	`cube-unmult_binary64_1820` `times-frac_binary64_1789`
7×	`difference-of-sqr-1_binary64_1753`
5×	`mul-1-neg_binary64_1775`
4×	`distribute-rgt-neg-out_binary64_1743` `associate-/l*_binary64_1728`
3×	`count-2_binary64_1731` `associate-*r/_binary64_1725`
1×	`unpow3_binary64_1849` `unpow2_binary64_1848` `unpow1_binary64_1841` `1-exp_binary64_1827` `mul0-lft_binary64_1765` `*-inverses_binary64_1763` `rgt-mult-inverse_binary64_1760`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `cos-neg_binary64_1914` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-pow_binary64_1872` `log-rec_binary64_1871` `log-div_binary64_1870` `log-prod_binary64_1869` `pow-base-0_binary64_1867` `unpow1/3_binary64_1850` `unpow1/2_binary64_1847` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `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-sqrt-square_binary64_1796` `rem-square-sqrt_binary64_1795` `div-sub_binary64_1788` `/-rgt-identity_binary64_1774` `mul0-rgt_binary64_1766` `div0_binary64_1764` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `remove-double-div_binary64_1759` `difference-of-squares_binary64_1752` `swap-sqr_binary64_1750` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `distribute-rgt-out--_binary64_1737` `distribute-lft-out--_binary64_1735` `associate-/r/_binary64_1729` `associate-/r_binary64_1727` `associate-l/_binary64_1726`

Counts

1 → 3

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	28	25
2	53	25
3	132	25
4	374	25
5	1289	25
6	3563	25

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.2b

Counts

4 → 1

Compiler

Compiled 68 to 40 computations (41.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.0b	(.f64 4 (.f64 b b))
0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite114.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`add-sqr-sqrt_binary64_1805`
11×	`*-un-lft-identity_binary64_1783` `add-log-exp_binary64_1822`
10×	`pow1_binary64_1844` `add-exp-log_binary64_1821`
9×	`add-cbrt-cube_binary64_1819`
8×	`add-cube-cbrt_binary64_1818`
3×	`unpow-prod-down_binary64_1862` `pow-unpow_binary64_1860` `pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `associate-l_binary64_1724` `cancel-sign-sub-inv_binary64_1749`
2×	`sum-log_binary64_1874` `diff-log_binary64_1875` `difference-of-squares_binary64_1752`
1×	`pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `unpow2_binary64_1848` `sqr-pow_binary64_1755` `unswap-sqr_binary64_1751` `associate-r_binary64_1723` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `flip-+_binary64_1757` `+-commutative_binary64_1713` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735` `associate--l+_binary64_1720`

Counts

4 → 68

Calls

4 calls:

11.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
6.0ms	(.f64 4 (.f64 b b))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 1861 to 857 computations (53.9% saved)

series1.1s (16.6%)

Error

0.0b

Counts

4 → 57

Calls

4 calls:

398.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
392.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
193.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
28.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 2455 to 2044 computations (16.7% saved)

simplify315.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-l_binary64_1724`
437×	`associate-r_binary64_1723`
359×	`cancel-sign-sub-inv_binary64_1749`
275×	`distribute-rgt-in_binary64_1733`
261×	`distribute-lft-in_binary64_1732`
247×	`distribute-rgt-neg-in_binary64_1741`
167×	`associate-+l+_binary64_1716`
147×	`sqr-pow_binary64_1755`
140×	`*-commutative_binary64_1714`
133×	`associate-+r+_binary64_1715`
113×	`+-commutative_binary64_1713`
106×	`sub-neg_binary64_1776`
101×	`exp-prod_binary64_1835`
83×	`unswap-sqr_binary64_1751`
78×	`pow-sqr_binary64_1756`
74×	`distribute-neg-in_binary64_1744`
73×	`log-prod_binary64_1869`
69×	`cube-prod_binary64_1811`
65×	`associate--l+_binary64_1720`
55×	`exp-sum_binary64_1829`
51×	`distribute-lft-neg-out_binary64_1742`
44×	`distribute-lft-neg-in_binary64_1740`
42×	`neg-sub0_binary64_1778`
41×	`distribute-rgt-out_binary64_1736`
38×	`pow-plus_binary64_1846`
37×	`neg-mul-1_binary64_1779`
30×	`unsub-neg_binary64_1777`
28×	`+-rgt-identity_binary64_1768`
27×	`*-rgt-identity_binary64_1773`
26×	`distribute-rgt-neg-out_binary64_1743`
25×	`*-lft-identity_binary64_1772` `swap-sqr_binary64_1750`
19×	`cube-unmult_binary64_1820`
18×	`associate-+r-_binary64_1717`
16×	`log-pow_binary64_1872` `difference-of-sqr--1_binary64_1754`
15×	`difference-of-sqr-1_binary64_1753`
13×	`mul-1-neg_binary64_1775`
12×	`distribute-rgt-out--_binary64_1737`
11×	`unpow3_binary64_1849` `associate-+l-_binary64_1718`
9×	`rem-sqrt-square_binary64_1796` `distribute-lft-out_binary64_1734`
8×	`pow-base-1_binary64_1843` `associate--r+_binary64_1719`
7×	`unpow2_binary64_1848`
6×	`unpow1_binary64_1841` `associate-/l/_binary64_1730` `associate-/l*_binary64_1728`
5×	`div-exp_binary64_1834` `cube-mult_binary64_1813` `associate-*r/_binary64_1725`
4×	`exp-diff_binary64_1831` `sub0-neg_binary64_1770` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
3×	`distribute-rgt1-in_binary64_1739` `count-2_binary64_1731`
2×	`prod-exp_binary64_1832` `rem-3cbrt-lft_binary64_1808` `rem-square-sqrt_binary64_1795` `distribute-lft1-in_binary64_1738` `associate-/r/_binary64_1729`
1×	`1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-3cbrt-rft_binary64_1809` `times-frac_binary64_1789` `/-rgt-identity_binary64_1774` `-inverses_binary64_1763` `rgt-mult-inverse_binary64_1760` `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` `unpow1/2_binary64_1847` `exp-to-pow_binary64_1845` `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` `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-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `div-sub_binary64_1788` `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_1762` `lft-mult-inverse_binary64_1761` `remove-double-div_binary64_1759` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `associate-*l/_binary64_1726` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

125 → 285

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	2656
1	331	2443
2	925	2422
3	3419	2422

prune403.0ms (6.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	283	2	285
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	283	3	286

Error

Counts

286 → 3

Compiler

Compiled 8536 to 4198 computations (50.8% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 b 4) (pow.f64 a 4))
0.0b	(+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
0.0b	(.f64 4 (.f64 b b))
2.2b	(.f64 (.f64 a a) (*.f64 b b))

rewrite155.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

37×	`pow1_binary64_1844`
21×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
17×	`pow-prod-down_binary64_1854`
11×	`prod-exp_binary64_1832` `add-log-exp_binary64_1822` `cbrt-unprod_binary64_1816`
9×	`*-un-lft-identity_binary64_1783`
6×	`add-sqr-sqrt_binary64_1805`
5×	`add-cube-cbrt_binary64_1818`
4×	`pow-prod-up_binary64_1853` `pow-plus_binary64_1846` `associate-l_binary64_1724` `sum-log_binary64_1874`
2×	`pow2_binary64_1864` `pow-sqr_binary64_1756` `unswap-sqr_binary64_1751` `associate-r_binary64_1723` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `flip-+_binary64_1757` `+-commutative_binary64_1713` `unpow-prod-down_binary64_1862` `distribute-lft-out_binary64_1734`
1×	`associate-+r+_binary64_1715`

Counts

4 → 74

Calls

4 calls:

20.0ms	(+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
9.0ms	(.f64 (.f64 a a) (*.f64 b b))
7.0ms	(+.f64 (pow.f64 b 4) (pow.f64 a 4))
6.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 2404 to 1318 computations (45.2% saved)

series630.0ms (9.8%)

Error

Counts

4 → 39

Calls

4 calls:

307.0ms	(+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
168.0ms	(+.f64 (pow.f64 b 4) (pow.f64 a 4))
81.0ms	(.f64 (.f64 a a) (*.f64 b b))
31.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 2211 to 1634 computations (26.1% saved)

simplify190.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

504×	`unswap-sqr_binary64_1751`
494×	`cancel-sign-sub-inv_binary64_1749`
476×	`*-commutative_binary64_1714`
327×	`distribute-rgt-neg-in_binary64_1741`
315×	`distribute-rgt-in_binary64_1733`
304×	`distribute-lft-neg-in_binary64_1740`
281×	`distribute-lft-in_binary64_1732`
191×	`associate-l_binary64_1724`
184×	`associate-r_binary64_1723`
181×	`sqr-pow_binary64_1755`
149×	`distribute-rgt-out_binary64_1736`
110×	`sub-neg_binary64_1776`
96×	`pow-sqr_binary64_1756`
91×	`exp-prod_binary64_1835`
86×	`distribute-neg-in_binary64_1744`
83×	`cube-prod_binary64_1811` `associate-+l+_binary64_1716`
76×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
74×	`associate-+r+_binary64_1715`
71×	`distribute-rgt-out--_binary64_1737`
48×	`+-commutative_binary64_1713`
47×	`difference-of-squares_binary64_1752`
46×	`log-prod_binary64_1869`
40×	`swap-sqr_binary64_1750`
39×	`unsub-neg_binary64_1777`
36×	`distribute-lft-neg-out_binary64_1742`
29×	`pow-plus_binary64_1846`
22×	`unpow3_binary64_1849`
20×	`associate-/l*_binary64_1728`
19×	`associate--l+_binary64_1720` `associate--r+_binary64_1719`
18×	`distribute-lft-out_binary64_1734`
17×	`associate-+r-_binary64_1717`
16×	`cube-unmult_binary64_1820` `cube-mult_binary64_1813`
14×	`+-rgt-identity_binary64_1768` `associate-+l-_binary64_1718`
13×	`prod-exp_binary64_1832`
11×	`distribute-rgt-neg-out_binary64_1743`
10×	`log-pow_binary64_1872`
8×	`sub0-neg_binary64_1770`
7×	`rem-sqrt-square_binary64_1796`
6×	`exp-lft-sqr_binary64_1838`
5×	`distribute-lft-out--_binary64_1735`
4×	`count-2_binary64_1731`
3×	`unpow1_binary64_1841` `exp-sum_binary64_1829`
2×	`unpow2_binary64_1848` `cancel-sign-sub_binary64_1748` `associate-/l/_binary64_1730` `associate-*r/_binary64_1725`
1×	`1-exp_binary64_1827` `/-rgt-identity_binary64_1774` `-rgt-identity_binary64_1773` `-inverses_binary64_1763` `rgt-mult-inverse_binary64_1760`
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` `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-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `div-exp_binary64_1834` `rec-exp_binary64_1833` `exp-diff_binary64_1831` `exp-neg_binary64_1830` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-div_binary64_1812` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `rem-square-sqrt_binary64_1795` `times-frac_binary64_1789` `div-sub_binary64_1788` `mul-1-neg_binary64_1775` `-lft-identity_binary64_1772` `remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `+-lft-identity_binary64_1767` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `div0_binary64_1764` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate-/r/_binary64_1729` `associate-/r_binary64_1727` `associate-*l/_binary64_1726` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

113 → 209

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	1772
1	310	1542
2	1242	1511
3	3000	1505

prune367.0ms (5.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	209	3	212

Error

Counts

212 → 3

Compiler

Compiled 7364 to 4147 computations (43.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
0.2b	(pow.f64 (.f64 b (.f64 b 4)) 3)
2.2b	(.f64 (.f64 a a) (*.f64 b b))
20.8b	(cbrt.f64 (pow.f64 (.f64 b (.f64 b 4)) 3))

rewrite193.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

38×	`pow1_binary64_1844`
22×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
17×	`pow-prod-down_binary64_1854`
11×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
9×	`add-log-exp_binary64_1822`
8×	`cbrt-prod_binary64_1814`
6×	`add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`pow-prod-up_binary64_1853` `pow-plus_binary64_1846`
3×	`pow-unpow_binary64_1860` `pow-pow_binary64_1855` `pow-exp_binary64_1851` `rem-cube-cbrt_binary64_1806` `sum-log_binary64_1874`
2×	`unpow-prod-down_binary64_1862` `unpow3_binary64_1849` `cube-mult_binary64_1813` `cube-prod_binary64_1811` `sqr-pow_binary64_1755` `pow2_binary64_1864` `pow-sqr_binary64_1756`
1×	`pow1/3_binary64_1865` `rem-cbrt-cube_binary64_1807` `unswap-sqr_binary64_1751` `associate-l_binary64_1724` `associate-r_binary64_1723` `*-commutative_binary64_1714` `pow-to-exp_binary64_1852` `flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-+r+_binary64_1715` `+-commutative_binary64_1713`

Counts

4 → 84

Calls

4 calls:

25.0ms	(+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
9.0ms	(.f64 (.f64 a a) (*.f64 b b))
6.0ms	(pow.f64 (.f64 b (.f64 b 4)) 3)
3.0ms	(cbrt.f64 (pow.f64 (.f64 b (.f64 b 4)) 3))

Compiler

Compiled 2983 to 1846 computations (38.1% saved)

series374.0ms (5.8%)

Error

Counts

4 → 24

Calls

4 calls:

171.0ms	(+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
86.0ms	(.f64 (.f64 a a) (*.f64 b b))
45.0ms	(pow.f64 (.f64 b (.f64 b 4)) 3)
43.0ms	(cbrt.f64 (pow.f64 (.f64 b (.f64 b 4)) 3))

Compiler

Compiled 1608 to 1310 computations (18.5% saved)

simplify168.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

596×	`unswap-sqr_binary64_1751`
488×	`*-commutative_binary64_1714`
278×	`distribute-rgt-in_binary64_1733`
254×	`distribute-lft-in_binary64_1732`
195×	`associate-l_binary64_1724`
173×	`associate-r_binary64_1723`
145×	`cancel-sign-sub-inv_binary64_1749`
110×	`exp-prod_binary64_1835`
102×	`log-prod_binary64_1869`
100×	`sqr-pow_binary64_1755`
85×	`associate-+l+_binary64_1716`
82×	`associate-+r+_binary64_1715`
80×	`cube-prod_binary64_1811` `distribute-rgt-neg-in_binary64_1741`
77×	`swap-sqr_binary64_1750`
76×	`distribute-lft-neg-in_binary64_1740`
57×	`pow-sqr_binary64_1756`
23×	`pow-plus_binary64_1846` `sub-neg_binary64_1776` `associate--r+_binary64_1719`
21×	`associate-/l*_binary64_1728`
20×	`distribute-neg-in_binary64_1744` `associate--l+_binary64_1720`
19×	`distribute-rgt-out_binary64_1736` `+-commutative_binary64_1713`
18×	`log-pow_binary64_1872`
17×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
14×	`distribute-lft-out_binary64_1734`
13×	`unpow3_binary64_1849` `cube-unmult_binary64_1820`
11×	`rem-sqrt-square_binary64_1796`
10×	`cube-mult_binary64_1813`
9×	`distribute-lft-neg-out_binary64_1742` `distribute-rgt-out--_binary64_1737` `associate-/l/_binary64_1730`
8×	`associate-*r/_binary64_1725`
7×	`count-2_binary64_1731` `associate-+l-_binary64_1718` `associate-+r-_binary64_1717`
6×	`prod-exp_binary64_1832`
5×	`unsub-neg_binary64_1777` `distribute-rgt-neg-out_binary64_1743`
3×	`unpow1_binary64_1841` `rem-cbrt-cube_binary64_1807` `distribute-lft-out--_binary64_1735`
2×	`unpow2_binary64_1848` `exp-lft-sqr_binary64_1838` `exp-sum_binary64_1829`
1×	`1-exp_binary64_1827` `rem-3cbrt-lft_binary64_1808` `-rgt-identity_binary64_1773` `-lft-identity_binary64_1772` `*-inverses_binary64_1763` `rgt-mult-inverse_binary64_1760` `difference-of-squares_binary64_1752` `associate-/r/_binary64_1729`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `cos-neg_binary64_1914` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-rec_binary64_1871` `log-div_binary64_1870` `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-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `div-exp_binary64_1834` `rec-exp_binary64_1833` `exp-diff_binary64_1831` `exp-neg_binary64_1830` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-div_binary64_1812` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-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` `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_1762` `lft-mult-inverse_binary64_1761` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate-/r_binary64_1727` `associate-l/_binary64_1726` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

108 → 285

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1648
1	299	1454
2	1267	1405

prune708.0ms (11%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	285	3	288

Error

Counts

288 → 3

Compiler

Compiled 11202 to 6855 computations (38.8% saved)

regimes352.0ms (5.5%)

Accuracy

Total 0.0b remaining (74.8%)

Threshold costs 0.0b (74.8%)

Compiler

Compiled 4537 to 3090 computations (31.9% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64_1714` `+-commutative_binary64_1713`
2×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778` `sub-neg_binary64_1776` `*-rgt-identity_binary64_1773`
1×	`1-exp_binary64_1827` `unsub-neg_binary64_1777` `distribute-rgt-neg-out_binary64_1743`
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` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `*-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-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	20	49
1	31	49
2	35	49
3	37	49
4	40	49
5	39	49

Proof

(=> (- f64 (+ f64 (+ f64 (* f64 2 (* f64 (* f64 h0 h0) (* f64 h1 h1))) (+ f64 (pow f64 h1 4) (pow f64 h0 4))) (* f64 (* f64 (cbrt f64 4) (cbrt f64 4)) (* f64 (cbrt f64 4) (* f64 h1 h1)))) 1))
sub-neg_binary64_1776 =>
(+ f64 (+ f64 (+ f64 (* f64 2 (* f64 (* f64 h0 h0) (* f64 h1 h1))) (+ f64 (pow f64 h1 4) (pow f64 h0 4))) (* f64 (* f64 (cbrt f64 4) (cbrt f64 4)) (=> (* f64 (cbrt f64 4) (* f64 h1 h1))))) (neg f64 1))
*-commutative_binary64_1714 =>
(+ f64 (+ f64 (+ f64 (* f64 2 (* f64 (* f64 h0 h0) (* f64 h1 h1))) (+ f64 (pow f64 h1 4) (pow f64 h0 4))) (* f64 (* f64 (cbrt f64 4) (cbrt f64 4)) (* f64 (* f64 h1 h1) (cbrt f64 4)))) (=> (neg f64 1)))
neg-mul-1_binary64_1779 =>
(+ f64 (+ f64 (+ f64 (* f64 2 (* f64 (* f64 h0 h0) (* f64 h1 h1))) (+ f64 (pow f64 h1 4) (pow f64 h0 4))) (* f64 (* f64 (cbrt f64 4) (cbrt f64 4)) (* f64 (* f64 h1 h1) (cbrt f64 4)))) (=> (* f64 -1 1)))
*-rgt-identity_binary64_1773 =>
(+ f64 (+ f64 (+ f64 (* f64 2 (* f64 (* f64 h0 h0) (* f64 h1 h1))) (+ f64 (pow f64 h1 4) (pow f64 h0 4))) (* f64 (* f64 (cbrt f64 4) (cbrt f64 4)) (* f64 (* f64 h1 h1) (cbrt f64 4)))) -1)

end0.0ms (0%)

sample1.1s (17.2%)

Algorithm

1×

intervals

Results

330.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 651 to 456 computations (30% saved)

Details

analyze73.0ms (1.1%)

sample19.0ms (0.3%)

simplify154.0ms (2.4%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite114.0ms (1.8%)

series1.1s (16.6%)

simplify315.0ms (4.9%)

prune403.0ms (6.2%)

localize17.0ms (0.3%)

rewrite155.0ms (2.4%)

series630.0ms (9.8%)

simplify190.0ms (2.9%)

prune367.0ms (5.7%)

localize20.0ms (0.3%)

rewrite193.0ms (3%)

series374.0ms (5.8%)

simplify168.0ms (2.6%)

prune708.0ms (11%)

regimes352.0ms (5.5%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.1s (17.2%)

Profiling