Details

analyze117.0ms (2.1%)

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%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify165.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4915	43
1	4915	43

prune3.0ms (0.1%)

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 58 to 38 computations (34.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.2b	(.f64 (.f64 b b) (+.f64 3 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
14×	`add-cbrt-cube_binary64_1819`
10×	`add-cube-cbrt_binary64_1818` `associate-r_binary64_1723`
6×	`distribute-lft-in_binary64_1732` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `cancel-sign-sub-inv_binary64_1749` `distribute-rgt-in_binary64_1733` `pow-prod-down_binary64_1854` `add-log-exp_binary64_1822`
4×	`associate-*r/_binary64_1725`
3×	`pow-unpow_binary64_1860` `unpow-prod-down_binary64_1862`
2×	`associate-+r+_binary64_1715` `difference-of-squares_binary64_1752` `flip-+_binary64_1757` `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` `distribute-lft-out--_binary64_1735` `sum-log_binary64_1874` `pow-pow_binary64_1855` `flip--_binary64_1758` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 87

Calls

4 calls:

10.0ms	(.f64 (.f64 a a) (-.f64 1 a))
9.0ms	(+.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 3 a)))))
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
7.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series161.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(+.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 3 a)))))
31.0ms	(.f64 (.f64 a a) (-.f64 1 a))
28.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
23.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5239	1789

prune148.0ms (2.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	3	100

Merged error: 0.0b

Counts

100 → 3

Compiler

Compiled 3517 to 1797 computations (48.9% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.1b	(.f64 a (.f64 b b))
0.2b	(.f64 (.f64 b b) (+.f64 3 a))
1.0b	(.f64 a (.f64 a (*.f64 b b)))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1_binary64_1844`
16×	`add-sqr-sqrt_binary64_1805`
15×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `*-un-lft-identity_binary64_1783` `pow-prod-down_binary64_1854`
12×	`associate-r_binary64_1723`
10×	`add-cube-cbrt_binary64_1818`
8×	`associate-l_binary64_1724`
6×	`cancel-sign-sub-inv_binary64_1749`
5×	`distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733`
4×	`associate-r/_binary64_1725` `-commutative_binary64_1714` `add-log-exp_binary64_1822`
3×	`unswap-sqr_binary64_1751`
2×	`difference-of-squares_binary64_1752` `sub-neg_binary64_1776`
1×	`flip3--_binary64_1787` `distribute-lft-out_binary64_1734` `flip-+_binary64_1757` `distribute-lft-out--_binary64_1735` `flip3-+_binary64_1786` `flip--_binary64_1758`

Counts

4 → 96

Calls

4 calls:

10.0ms	(.f64 (.f64 a a) (-.f64 1 a))
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
8.0ms	(.f64 a (.f64 a (*.f64 b b)))
6.0ms	(.f64 a (.f64 b b))

series107.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(.f64 (.f64 a a) (-.f64 1 a))
29.0ms	(.f64 a (.f64 a (*.f64 b b)))
23.0ms	(.f64 (.f64 b b) (+.f64 3 a))
23.0ms	(.f64 a (.f64 b b))

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4929	1111
1	4929	1111

prune186.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	108	3	111

Merged error: 0.0b

Counts

111 → 3

Compiler

Compiled 4422 to 2497 computations (43.5% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 b b) (+.f64 a 3))
0.3b	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
30.0b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1783`
14×	`add-sqr-sqrt_binary64_1805`
13×	`add-cube-cbrt_binary64_1818`
12×	`cbrt-prod_binary64_1814`
11×	`add-exp-log_binary64_1821` `pow1_binary64_1844`
10×	`add-cbrt-cube_binary64_1819`
9×	`unpow-prod-down_binary64_1862`
6×	`pow-unpow_binary64_1860` `cube-prod_binary64_1811`
4×	`cube-div_binary64_1812` `add-log-exp_binary64_1822` `associate-r_binary64_1723`
3×	`sqr-pow_binary64_1755` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854`
2×	`associate-*r/_binary64_1725` `cube-mult_binary64_1813` `unpow3_binary64_1849` `cbrt-div_binary64_1815` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `distribute-lft-in_binary64_1732` `distribute-lft-out_binary64_1734` `unpow2_binary64_1848` `associate-l_binary64_1724` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `pow1/3_binary64_1865` `unswap-sqr_binary64_1751`

Counts

4 → 90

Calls

4 calls:

11.0ms	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
9.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))
9.0ms	(.f64 (.f64 b b) (+.f64 a 3))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series753.0ms (13.5%)

Counts

4 → 12

Calls

4 calls:

626.0ms	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
78.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))
26.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
22.0ms	(.f64 (.f64 b b) (+.f64 a 3))

simplify98.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4986	3655
1	4986	3655

prune182.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0.0b

Counts

105 → 3

Compiler

Compiled 4359 to 2320 computations (46.8% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) 16))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
3.4b	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) 16)))
31.3b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) 16))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))))))

rewrite110.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`associate-*r/_binary64_1725`
56×	`frac-add_binary64_1791`
48×	`associate-*l/_binary64_1726`
42×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
36×	`frac-times_binary64_1793`
31×	`flip3--_binary64_1787` `flip--_binary64_1758`
15×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
12×	`add-exp-log_binary64_1821`
11×	`add-cbrt-cube_binary64_1819`
10×	`pow1_binary64_1844`
9×	`times-frac_binary64_1789`
6×	`add-log-exp_binary64_1822`
3×	`associate-/l_binary64_1728` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-unpow_binary64_1860` `unpow-prod-down_binary64_1862` `associate-/r_binary64_1727` `associate-l_binary64_1724` `pow-prod-down_binary64_1854`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729`
1×	`div-sub_binary64_1788` `sqr-pow_binary64_1755` `unpow2_binary64_1848` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `pow-pow_binary64_1855` `clear-num_binary64_1782` `pow-to-exp_binary64_1852` `sub-neg_binary64_1776` `pow-exp_binary64_1851` `associate-r*_binary64_1723`

Counts

4 → 128

Calls

4 calls:

35.0ms	(.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) 16))
16.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) 16))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))))))
9.0ms	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) 16)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series799.0ms (14.3%)

Counts

4 → 12

Calls

4 calls:

359.0ms	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) 16)))
318.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) 16))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))))))
93.0ms	(.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) (.f64 (+.f64 (.f64 (.f64 b b) (+.f64 a 3)) (-.f64 (.f64 a a) (pow.f64 a 3))) 16))
29.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify140.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5000	13790

prune758.0ms (13.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	140	3	143

Merged error: 0b

Counts

143 → 3

Compiler

Compiled 15244 to 7989 computations (47.6% saved)

regimes269.0ms (4.8%)

Compiler: Compiled 5028 to 2969 computations (41% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	55
1	57	55

end0.0ms (0%)

sample1.2s (21.3%)

Algorithm

1×

intervals

Results

485.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 899 to 539 computations (40% saved)

Details

analyze117.0ms (2.1%)

sample26.0ms (0.5%)

simplify165.0ms (3%)

prune3.0ms (0.1%)

localize15.0ms (0.3%)

rewrite44.0ms (0.8%)

series161.0ms (2.9%)

simplify56.0ms (1%)

prune148.0ms (2.7%)

localize22.0ms (0.4%)

rewrite44.0ms (0.8%)

series107.0ms (1.9%)

simplify88.0ms (1.6%)

prune186.0ms (3.3%)

localize19.0ms (0.3%)

rewrite46.0ms (0.8%)

series753.0ms (13.5%)

simplify98.0ms (1.8%)

prune182.0ms (3.3%)

localize25.0ms (0.4%)

rewrite110.0ms (2%)

series799.0ms (14.3%)

simplify140.0ms (2.5%)

prune758.0ms (13.6%)

regimes269.0ms (4.8%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (21.3%)

Profiling