Details

analyze137.0ms (0.1%)

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%	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)

sample24.0ms (0%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify234.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4912	46
1	4912	46

prune3.0ms (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

Merged error: 0.2b

Counts

2 → 1

Compiler

Compiled 62 to 42 computations (32.3% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 a a) (+.f64 1 a))
0.1b	(+.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))))))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

13.0ms	(.f64 (.f64 a a) (+.f64 1 a))
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 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series324.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(+.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))))))
66.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
66.0ms	(.f64 (.f64 a a) (+.f64 1 a))
48.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify43.0ms (0%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5113	1848

prune154.0ms (0.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	4	93

Merged error: 0.0b

Counts

93 → 4

Compiler

Compiled 3566 to 1934 computations (45.8% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 a a) (+.f64 1 a))
0.1b	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
1.7b	(.f64 (.f64 b b) (*.f64 a a))

rewrite67.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_1844`
32×	`associate-*r/_binary64_1725`
26×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
20×	`frac-add_binary64_1791` `pow-prod-down_binary64_1854`
14×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `flip3-+_binary64_1786`
13×	`add-log-exp_binary64_1822`
8×	`add-sqr-sqrt_binary64_1805` `-un-lft-identity_binary64_1783` `associate-r*_binary64_1723`
6×	`add-cube-cbrt_binary64_1818` `sum-log_binary64_1874`
5×	`flip3--_binary64_1787` `flip--_binary64_1758`
4×	`distribute-lft-in_binary64_1732` `pow-plus_binary64_1846` `pow-prod-up_binary64_1853` `distribute-rgt-in_binary64_1733`
3×	`associate-l_binary64_1724` `*-commutative_binary64_1714` `unswap-sqr_binary64_1751`
2×	`associate-+r+_binary64_1715` `cancel-sign-sub-inv_binary64_1749` `pow-sqr_binary64_1756` `sub-neg_binary64_1776` `pow2_binary64_1864`
1×	`+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `associate-+l+_binary64_1716`

Counts

4 → 106

Calls

4 calls:

18.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
9.0ms	(.f64 (.f64 b b) (*.f64 a a))
9.0ms	(.f64 (.f64 a a) (+.f64 1 a))

series317.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
69.0ms	(.f64 (.f64 a a) (+.f64 1 a))
66.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
42.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5026	4891

prune294.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0.0b

Counts

122 → 4

Compiler

Compiled 6754 to 3970 computations (41.2% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (.f64 (.f64 a a) (+.f64 1 a)) 3)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
25.5b	(cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1 a)) 3))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64_1821` `pow1_binary64_1844`
15×	`add-cbrt-cube_binary64_1819`
10×	`add-sqr-sqrt_binary64_1805`
9×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
8×	`cbrt-prod_binary64_1814`
6×	`associate-*r/_binary64_1725` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-unpow_binary64_1860` `pow-prod-down_binary64_1854`
5×	`unpow-prod-down_binary64_1862`
4×	`pow-pow_binary64_1855` `cube-div_binary64_1812` `pow-exp_binary64_1851` `add-log-exp_binary64_1822`
3×	`sqr-pow_binary64_1755` `rem-cube-cbrt_binary64_1806` `associate-r_binary64_1723`
2×	`distribute-lft-in_binary64_1732` `cube-mult_binary64_1813` `flip-+_binary64_1757` `unpow3_binary64_1849` `cbrt-div_binary64_1815` `cancel-sign-sub-inv_binary64_1749` `distribute-rgt-in_binary64_1733` `flip3-+_binary64_1786` `pow-to-exp_binary64_1852` `sub-neg_binary64_1776` `cube-prod_binary64_1811`
1×	`flip3--_binary64_1787` `rem-cbrt-cube_binary64_1807` `unpow2_binary64_1848` `associate-l_binary64_1724` `*-commutative_binary64_1714` `pow1/3_binary64_1865` `unswap-sqr_binary64_1751` `flip--_binary64_1758`

Counts

4 → 89

Calls

4 calls:

9.0ms	(pow.f64 (.f64 (.f64 a a) (+.f64 1 a)) 3)
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
3.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1 a)) 3))

series218.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
65.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1 a)) 3))
51.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
24.0ms	(pow.f64 (.f64 (.f64 a a) (+.f64 1 a)) 3)

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4976	1481
1	4976	1481

prune176.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	101	4	105

Merged error: 0.0b

Counts

105 → 4

Compiler

Compiled 4109 to 2338 computations (43.1% saved)

localize39.0ms (0%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 a 3)))
1.3b	(+.f64 (pow.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) 3) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3))
5.6b	(+.f64 (.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))))))
41.8b	(/.f64 (+.f64 (pow.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) 3) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3)) (+.f64 (.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))))))))

rewrite3.0s (2%)

Algorithm

1×	rewrite-expression-head

Rules

7418×	`associate-*r/_binary64_1725`
3560×	`frac-add_binary64_1791`
3340×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
2176×	`frac-times_binary64_1793`
1344×	`frac-sub_binary64_1792`
1049×	`flip3--_binary64_1787` `flip--_binary64_1758`
834×	`associate-/r/_binary64_1729`
512×	`associate-*l/_binary64_1726`
48×	`cube-div_binary64_1812`
37×	`*-un-lft-identity_binary64_1783`
35×	`distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733`
28×	`associate-+r+_binary64_1715`
20×	`add-sqr-sqrt_binary64_1805`
19×	`add-cube-cbrt_binary64_1818`
18×	`cancel-sign-sub-inv_binary64_1749`
15×	`times-frac_binary64_1789`
14×	`associate-/l/_binary64_1730`
11×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
9×	`distribute-lft-out_binary64_1734` `pow1_binary64_1844`
8×	`associate--l+_binary64_1720` `add-log-exp_binary64_1822`
6×	`sub-neg_binary64_1776`
5×	`associate-/l*_binary64_1728` `sum-cubes_binary64_1784`
3×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `associate-/r_binary64_1727` `pow-prod-down_binary64_1854` `associate-r*_binary64_1723`
2×	`+-commutative_binary64_1713` `associate-+l+_binary64_1716` `sum-log_binary64_1874`
1×	`div-inv_binary64_1780` `associate-l_binary64_1724` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `unswap-sqr_binary64_1751`

Counts

4 → 1806

Calls

4 calls:

150.0ms	(/.f64 (+.f64 (pow.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) 3) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3)) (+.f64 (.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))))))))
85.0ms	(+.f64 (.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))))))
32.0ms	(+.f64 (pow.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) 3) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 a 3)))

series3.7s (2.5%)

Counts

4 → 12

Calls

4 calls:

1.6s	(+.f64 (pow.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) 3) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3))
1.1s	(/.f64 (+.f64 (pow.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) 3) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3)) (+.f64 (.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))))))))
865.0ms	(+.f64 (.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 (.f64 b a) (.f64 b a)) 2)))))))
71.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 a 3)))

simplify6.0s (4%)

Algorithm

1×	egg-herbie

Counts

1818 → 1818

Iterations

Useful iterations: 0 (163.0ms)

Iter	Nodes	Cost
0	5143	915275

Details

analyze137.0ms (0.1%)

sample24.0ms (0%)

simplify234.0ms (0.2%)

prune3.0ms (0%)

localize17.0ms (0%)

rewrite48.0ms (0%)

series324.0ms (0.2%)

simplify43.0ms (0%)

prune154.0ms (0.1%)

localize24.0ms (0%)

rewrite67.0ms (0%)

series317.0ms (0.2%)

simplify99.0ms (0.1%)

prune294.0ms (0.2%)

localize22.0ms (0%)

rewrite38.0ms (0%)

series218.0ms (0.1%)

simplify77.0ms (0.1%)

prune176.0ms (0.1%)

localize39.0ms (0%)

rewrite3.0s (2%)

series3.7s (2.5%)

simplify6.0s (4%)

prune2.2min (90%)

Profiling